Thesis Defense
Thursday May 20th, 2021
Time: 11:00 AM
Title: The Nirenberg Problem for Conical Singularities
Speaker: Lisandra Hernandez-Vazquez, Stony Brook University
Abstract:
We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2π$, the main result being sufficient conditions for a positive function of class at least $C^2$ to be the Gaussian curvature of such a conformal conical metric on the round sphere. Our methods particularly differ from the variational approach in that they don’t rely on the Moser-Trudinger inequality. Along the way, we also prove a general precompactness theorem for compact Riemann surfaces with at least three conical singularities and angles less than $2π$.