Research


My topics of research are the study of nonlinear problems that arise in mathematical physics, differential geometry and in some models of chemotaxis, with emphasis on the question of existence and uniqueness of solutions. These questions are closely related to optimal exponential Sobolev inequalities, and in many cases they present a lack of compactness that require new tools in Morse theory to detect the existence of critical points.

Recent Publications
  • Harnack inequalities and quantization properties for the n-Liouville equation, ArXiv: 2111.11781 (with P. Esposito).
  • Donaldson Functional in Teichmüller Theory, Int. Math. Res. Not. IMRN, 2022, to appear (with G. Tarantello and
    • and Z. Huang).
  • Nondegeneracy of solutions for a class of cooperative systems on Rn, Commun. Pure Appl. Anal. 20 (2021),
    • 4177–4193 (with G. Sweers).
  • Bifurcation for minimal surface equation in hyperbolic 3-manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 38
    • (2021), 243–279 (with G. Tarantello and Z. Huang).
  • Some results related to Schiffer’s Problem, J. Anal. Math. 142 (2020), 667-696 (with B. Kawohl).
  • Mountain pass solutions for nonsmooth elliptic problems, Minimax Theory Appl. 5 (2020), 129-150 (with F. Schuricht).

List of Publications (PDF file)


Selected Seminars and Conferences
  • Summer School in Cagliari, Graduate lectures series on:
  • Sanya International Forum, ``Frontiers of Geometry and analysis of Teichmüller space”, 01/2020
  • Princeton University Nonlinear analysis seminar, 12/2019
  • Plenary talk in ``Variational Problems arising from Physics and Geometry"
    • Rauischholzhausen Castle, Germany, 07/2018
  • Plenary talk in Conference in Honor of Prof. Abbas Bahri, Tunisia, 05/2015

Full List of talks given (PDF file)



Graduate Students
  • Samuel Magill, current Phd student
  • Edger Sterjo, CUNY Graduate Center, Ph.D. 2018
    • Infinitely many solutions to asymmetric, polyharmonic Dirichlet problems
      • Publication related to the thesis:
    • E. Sterjo, Multiplicity of solutions for polyharmonic Dirichlet problems with exponential nonlinearities and broken symmetry, Topol. Methods Nonlinear Anal. 50 (2017), 27–63.

Graduate MA Students
  • Mikhail Shklyar, M.A. 2016
  • Brian Sulkow, M.A. 2012