Hee Oh

Abraham Robinson Professor of Mathematics
photo of Hee Oh
Euclidean traveler
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time
- from Little Gidding by T.S. Eliot
Paper mail Department of Mathematics
Yale University.
PO Box 208283
New Haven, CT 06520-8283
U.S.A.
E-mail hee.oh(AT)yale(DOT)edu
Phone (203) 432-4193
Office KT 751

Publications and preprints

For the link to my papers in MathSciNet, click here or here. For preprints, versions here are more updated than those available in the arXiv.
    1. Deformations of Anosov subgroups: limit cones and growth indicators.
      (with S. Dey), Preprint (arXiv:2411.04020). (pdf)
    2. Zariski dense non-tempered subgroups in higher rank of nearly optimal growth.
      (with M. Fraczyk), Preprint (arXiv:2410.19551). (pdf)
    3. Bi-Lipschitz rigidity of discrete subgroups.
      (with R. Canary and A. Zimmer), Preprint (arXiv:2405.00249) (pdf)
    4. Relatively Anosov groups: finiteness, measure of maximal entropy and reparameterization.
      (with D. Kim), Preprint (arXiv:2404.09475) (pdf)
    5. Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications
      (with S. Dey and D. Kim), Preprint (arXiv:2401.12398) (pdf)
    6. Multiple correlations of spectra for higher rank Anosov representations.
      (with M. Chow), Preprint (arXiv:2403.05375) (pdf)
    7. Jordan and Cartan spectra in higher rank with applications to correlations.
      (with M. Chow), Preprint (arXiv:2308.16329) (pdf)
    8. Ergodic dichotomy for subspace flows in higher rank.
      (with D. Kim and Y. Wang), Preprint (arXiv:2310.19976) (pdf)
    9. Properly discontinuous actions, growth indicators and conformal measures for transverse subgroups.
      (with D. Kim and Y. Wang), Preprint (arXiv:2306.06846), (pdf)
    10. Non-concentration property of Patterson-Sullivan measures for Anosov subgroups.
      (with D. Kim), Preprint (arXiv:2304.14911), To appear in Ergodic Theory and Dynamical Systems (pdf)
    11. Infinite volume and atoms at the bottom of the spectrum.
      (with S. Edwards, M. Fraczyk, M. Lee), Preprint (arXiv:2304.14565), To appear in Comptes Rendus Mathématique (pdf)
    12. Conformal measure rigidity for representations via self-joinings.
      (with D. Kim), Advances in Math. 458 (2024), part B, Paper No.109992 (pdf)
    13. Rigidity of Kleinian groups via self-joinings: measure theoretic criterion.
      (with D. Kim), Preprint (arXiv:2302.03552) (pdf, video)
    14. Rigidity of Kleinian groups via self-joinings.
      (with D. Kim), Inventiones Mathematicae, Vol 234, issue 3 (2023), 937-948 (pdf, video)
    15. Torus counting and self-joinings of Kleinian groups.
      (with S. Edwards and M. Lee), J. Reine Angew. Math. 807 (2024), 151-185. (journal) . (pdf)
    16. Euclidean traveller in hyperbolic worlds.
      Notices Amer. Math. Soc. 69 (2022), no. 11, 1888-1897 (pdf , video)
    17. Dichotomy and measures on limit sets of Anosov groups.
      (with M. Lee), Int. Math. Res. Not. IMRN (2024), no. 7, 5658-5688 (pdf)
    18. Temperedness of L^2(\Gamma\G) and positive eigenfunctions in higher rank.
      (with S. Edwards), Communications of the AMS, Vol 3 (2023), 744-778 (pdf)
    19. On denseness of horospheres in higher rank homogeneous spaces.
      (with O. Landesberg),Ergodic Theory and Dynamical Systems, Vol 44 (2024), 3272-3289 (pdf)
    20. Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds.
      (with D. Kim and Y. Minsky), Journal of Modern Dynamics, Vol 19 (2023), 433-453 (pdf)
    21. Tent property of the growth indicator functions and applications.
      (with D. Kim and Y. Minsky), Geom. Dedicata 218 (2024), Paper No: 14 (pdf)
    22. Uniqueness of conformal measures and local mixng for Anosov groups.
      (with S. Edwards and M. Lee), Michigan Math. J. 72 (Prasad volume), 243-259 (2022) (pdf)
    23. Horospherical invariant measures and a rank dichotomy for Anosov groups.
      (with O. Landesberg, M. Lee, and E. Lindenstrauss), Journal of Modern Dynamics, Vol 19 (2023), pp.331-362 (pdf, video)
    24. The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups.
      (with M. Burger, O. Landesberg, and M. Lee), Journal of Modern Dynamics, Vol 19 (2023), pp. 301-330 (pdf, video)
    25. Ergodic decompositions of geometric measures on Anosov homogeneous spaces.
      (with M. Lee), Israel J. Math, Vol 260 (2024), pp. 195-234 (pdf, video)
    26. Invariant measures for horospherical actions and Anosov groups.
      (with M. Lee), Int. Math. Res. Notices, Vol 2023, No 19, pp. 16226--16295 (pdf, video part 1, video part 2)
    27. Anosov groups: local mixing, counting, and equidistribution.
      (with S. Edwards and M. Lee), Geometry & Topology, 27 (2023), 513-573 (pdf)
    28. Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds.
      (with S. Edwards), Duke Math. J, Vol 170 (2021), 3417-3458 (pdf)
    29. Isolations of geodesic planes in the frame bundle of a hyperbolic 3-manifold.
      (with A. Mohammadi), Compositio Math. Vol 159 (2023), 488-529 (pdf)
    30. Dynamics for discrete subgroups of SL(2,C).
      In: Dynamics, Geometry, Number theory: The impact of Margulis on Modern Mathematics (pdf)
    31. Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1).
      (with M. Lee), Journal of Modern Dynamics, Vol 15 (2019), 263--276 (pdf)
    32. Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends.
      (with M. Lee), To appear in Geometry & Topology, 101 pages, arXiv:1902.06621 (pdf , video).
    33. Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds.
      (with D. Kelmer), Journal of Modern Dynamics, Vol 17 (2021), 401--434 (pdf)
    34. Orbit closures for the PSL(2,R)-action on hyperbolic 3-manifolds.
      (Fields Institute Summer School Lecture Notes), Preprint, Not for publication (pdf)
    35. Geodesic planes in geometrically finite acylindrical 3-manifolds.
      (with Y. Benoist), Ergodic Theory and Dynamical Systems, Vol 42 (2022), 514--553 (memorial volume for Katok) (pdf , video)
    36. Geodesic planes in the convex core of an acylindrical 3-manifold.
      (with C. McMullen and A. Mohammadi), Duke. Math. J, 171 (2022), no. 5, 1029-1060. (pdf , video , Bourbaki video)
    37. Local mixing and invariant measures for horospherical subgroups on abelian covers.
      (with W. Pan), IMRN 2019, Issue 19, 6036-6088 (pdf)
    38. Remembering Marina Ratner.
      AMS Notices Amer. Math. Soc. 66 (2019), No. 3, p. 385 (pdf)
    39. Prime number theorems and holonomies for hyperbolic rational maps.
      (with D. Winter), Inventiones Mathematicae, Vol 208 (2017), 401--440 (pdf , video)
    40. Horocycles in hyperbolic 3-manifolds.
      (with C. McMullen and A. Mohammadi), Geometric and Functional Analsis, Vol 26 (2016), 961--973 (pdf)
    41. Geodesic planes in hyperbolic 3-manifolds.
      (with C. McMullen and A. Mohammadi), Inventiones Mathematicae, Vol 209 (2017), 425--461 (pdf , video)
    42. Invariant Radon measures for unipotent flows and products of Kleinian groups.
      (with A. Mohammadi), PAMS. 146 (2018), 1469--1479 (pdf)
    43. Fuchsian groups and compact hyperbolic surfaces.
      (with Y. Benoist), L'Enseignement Mathématique, Vol 62 (2016), 189--198 (pdf)
    44. Uniform congruence counting for Schottky semigroups in SL_2(Z).
      (with M. Magee and D. Winter), J. Reine Angew. Math., Vol 753 (2019), 89--135 (pdf)
    45. Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z).
      (with D. Winter), Journal of the American Mathematical Society, Vol 29 (2016), 1069--1115 (pdf)
    46. Closed geodesics and holonomies for Kleinian manifolds.
      (with G. Margulis and A. Mohammadi), Geometric and Functional analysis, Vol 24 (2014), 1608--1636 (pdf , video)
    47. Classification of joinings for Kleinian groups.
      (with A. Mohammadi), Duke Math.J., Vol 165 (2016), 2155--2223 (pdf , video)
    48. Matrix coefficients, counting and primes for orbits of geometrically finite groups.
      (with A. Mohammadi), Journal of the European Mathematical Society, Vol 17 (2015), 837--897 (pdf)
    49. Ergodicity of unipotent flows and Kleinian groups.
      (with A. Mohammadi), Journal of the American Mathematical Society, Vol 28 (2015), 531--577 (pdf , video)
    50. Eigenvalues of congruence covers of geometrically finite hyperbolic manifolds.
      Journal of Geometric Analysis, Vol 25 (2015), 1421--1430 (pdf)
    51. Counting visible circles on the sphere and Kleinian groups.
      (with N. Shah), LMS series Vol 425, 272--288. (pdf)
    52. Apollonian circle packings: dynamics and number theory.
      Japanese Journal of Math., Vol 9 (2014), 69--97, (expanded version of the 13th Takagi Lecture series notes). (pdf, video part 1, video part 2)
    53. Harmonic analysis, ergodic theory and counting for thin groups.
      In "Thin groups and superstrong approximation", MSRI publ.61 Cambridge Univ. Press. 2014 (pdf)
    54. Limits of translates of divergent geodesics and integral points on one-sheeted hyperboloids.
      (with N. Shah), Israel J. Math., Vol 199 (2014), pp. 915--931 (pdf)
    55. Effective circle count for Apollonian packings and closed horospheres.
      (with M. Lee), Geometric and Functional analysis, Vol 23 (2013), 580--621 (pdf)
    56. Equidistribution and counting for orbits of geometrically finite hyperbolic groups.
      (with N. Shah), Journal of the American Mathematical Society, Vol 26 (2013), 511--562 (pdf)
    57. The asymptotic distribution of circles in the orbits of Kleinian groups.
      (with N. Shah), Inventiones Mathematicae, Vol 187 (2012), 1--35 (pdf)
    58. On the distribution of orbits of geometrically finite hyperbolic groups on the boundary.
      (with S. Lim), Ergod. Th. & Dynam. Sys., Vol 32, 173--189 (2012) (pdf)
    59. Almost prime Pythagorean triples in thin orbits.
      (with A. Kontorovich), J. Reine Angew. Math. Vol 667 (2012), 89--131 (pdf)
    60. Effective equidistribution of S-integral points on symmetric varieties.
      (with Y. Benoist), Annales de L'Institut Fourier, Vol 62 (2012), 1889--1942 (pdf )
    61. Apollonian circle packings and closed horospheres on hyperbolic 3 manifolds.
      (with A. Kontorovich), Journal of the American Mathematical Society 24 (2011), 603--648 (pdf)
    62. Rational points on homogeneous varieties and equidistribution of adelic periods.
      (with A. Gorodnik), Geometric and Functional Analysis, Vol 21 (2011), 319--392 (pdf)
    63. Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond.
      Proceedings of International Congress of Mathematicians (2010), Vol III, 1308--1331 (pdf)
    64. Discreteness criterion for subgroups of products of SL(2).
      (with Y. Benoist), Transformation Groups, Vol 15 (2010), 503--515 (pdf)
    65. Orbital counting via mixing and unipotent flows.
      in Homogeneous flows, Moduli Spaces and Arithmetic, Clay Mathematics Proceedings, 2010, Vol 10, 339--375 (pdf)
    66. Strong wavefront lemma and counting lattice points in sectors.
      (with A. Gorodnik and N. Shah), Israel J. Math., Vol 176 (2010), 419--444 (pdf)
    67. Discrete subgroups of SL_3(R) generated by triangular matrices.
      (with Y. Benoist), Int. Math. Res. Notices, Article ID 149, 2009 (pdf)
    68. Integral points on symmetric varieties and Satake compactifications.
      (with A. Gorodnik and N. Shah), American J. Math., Vol 131 (2009), 1--57 (pdf)
    69. Manin's and Peyre's conjectures on rational points and adelic mixing.
      (with A. Gorodnik and F. Maucourant), Ann. Sci. Ecole Norm. Sup. Vol 41 (2008) 47--97 (pdf)
    70. Polar decomposition for p-adic symmetric spaces.
      (with Y. Benoist), Int. Math. Res. Notices (2007), Article ID 121 (pdf)
    71. Equidistribution of rational matrices in their conjugacy classes.
      (with Y. Benoist), Geom. and Funct. Analysis, Vol 17 (2007) (pdf)
    72. Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary.
      (with A. Gorodnik), Duke Math. J. Vol 139 (2007), 483--525 (pdf)
    73. Representations of integers by an invariant polynomial and unipotent flows.
      (with A. Eskin), Duke Math. J., Vol 135 (2006), 481--506 (pdf)
    74. Ergodic theoretic proof of equidistribution of Hecke points.
      (with A. Eskin), Erg. The & Dyn. Sys, Vol 26 (2006), 163--167 (pdf)
    75. On uniform exponential growth for linear groups.
      (with A. Eskin and S. Mozes), Inventiones Math. Vol 160 (2005), 1--30 (pdf)
    76. Lattice action on finite volume homogeneous spaces.
      J. Korean Math. Soc., Vol 42 (2005), 635--653 (pdf)
    77. The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group.
      Israel J. Math (Furstenberg volume), Vol 149 (2005), 301--316 (pdf)
    78. On a problem concerning arithmeticity of discrete groups acting on H...H.
      In "Algebraic groups and Arithmetic" (TIFR, India) (pdf)
    79. Harmonic analysis and Hecke operators.
      In "Rigidity in Dynamics and Geometry", Springer-Verlag, edited by Burger and Iozzi (pdf)
    80. Hardy-Littlewood system and representations of integers by an invariant polynomial.
      Geom. and Funct. Analysis, Vol 14 (2004) 791--809 (pdf)
    81. Finiteness of compact maximal flats of bounded volume.
      Ergod. Th and Dynam. Sys. Vol 24 (2004), 217--225 (pdf)
    82. Cartan decomposition subgroups of SO(2,n).
      (with D. Witte), Trans. AMS Vol 356 (2004) 1--38 (pdf)
    83. Equidistribution of integer points on a family of homogeneous varieties: a problem of Linnik.
      (with W. Gan), Compositio Math. Vol 136 (2003), 323--352 (pdf)
    84. Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants.
      Duke Math. J., vol 113 (2002), pp. 133--192 (pdf)
    85. Uniform exponential growth for linear groups. (announcement)
      (with A. Eskin and S. Mozes) Int. Math. Res. Not. no 31 (2002), 1675--1683
    86. Compact Clifford-Klein forms of homogeneous spaces of SO(2,n).
      (with D. Witte), Geom. Dedicata, vol 89 (2002), 25–57 (pdf)
    87. Hecke operators and equidistribution of Hecke points.
      (with L. Clozel and E. Ullmo), Inventiones Math., vol 144 (2001), pp. 327--351 (pdf)
    88. Adelic version of Margulis arithmeticity theorem.
      Math. Ann. vol 321 (2001), 4, pp. 789--815 (pdf)
    89. New examples of compact Clifford-Klein forms of homogeneous spaces of SO(2,n).
      (with Dave Witte), IMRN, 2000, no 5, pp. 235--251 (pdf)
    90. S-arithmeticity of discrete subgroups containing lattices in horospherical subgroups.
      Duke Math. J., vol 101 (2000), pp. 209--219
    91. On discrete subgroups containing a lattice in a horospherical subgroup.
      Israel J. of Math., vol 110 (1999), pp. 333--340 (pdf)
    92. Tempered subgroups and representations with minimal decay of matrix coefficients.
      Bull. Math. Soc. France, vol 126 (1998), pp. 355--380 (pdf) Minor correction: (pdf)
    93. Discrete subgroups generated by lattices in opposite horospherical subgroups.
      J. Algebra, vol 203 (1998), pp. 621--676 (pdf)
    94. Arithmetic properties of some Zariski dense subgroups.
      Proceedings of International Colloquium on "Lie groups and Ergodic theory" in TIFR, Bombay, 1996
    95. Discrete subgroups of SL_n(R) generated by lattices in horospherical subgroups.
      C. R. Acad. Sci. Paris, Series I, vol 323 (1996), pp. 1219--1224 (pdf)