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 $2π$. |