Research

Publications

  • “Riemannian Anosov extension and applications” (with Alena Erchenko and Andrey Gogolev),
    Journal de l’École polytechnique – Mathématiques, Volume 10 (2023), 945-987.
  • “Flexibility of sections of nearly integrable Hamiltonian systems” (with Dmitri Burago and Sergei Ivanov),
    Communications in Contemporary Mathematics, 25 (2023), no. 4, Paper No. 2250028.
  • “Finsler perturbation with non-dense geodesics with irrational directions” (with Dmitri Burago),
    Asian Journal of Mathematics, 25 (2021), no. 5, 715-726.
  • “Properties of equilibrium states for geodesic flows without focal points” (with Lien-Yung Kao and Kiho Park),
    Advances in Mathematics, 380 (2021), 107564.
  • “Unique equilibrium states for geodesic flows over surfaces without focal points” (with Lien-Yung Kao and Kiho Park),
    Nonlinearity, 33 (2020), no. 3, 1118-1155.
  • “On total flexibility of local structures of Finsler tori without conjugate points”,
    Journal of Topology and Analysis, Vol. 11 (2019), No. 02, 349-355.
  • “Positive metric entropy arises in some nondegenerate nearly integrable systems”,
    Journal of Modern Dynamics, Vol. 11 (2017), 43-56.
  • On the Cclosing lemma for Hamiltonian flows on symplectic 4-manifolds”, under review.
  • A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature” (with Keith Burns), under review. 
  • Pressure gaps, geometric potentials, and nonpositively curved manifolds (with Lien-Yung Kao and Kiho Park), under review.
  • “Elementary Introduction to Modern Geometry” (joint with Dmitri Burago and Yuri Burago), an invited book designed to be a text for researchers, graduate students and advanced undergraduate students studying modern geometry. In preparation.