# Curvature Functions for Compact 2-Manifolds

@article{Kazdan1974CurvatureFF,
title={Curvature Functions for Compact 2-Manifolds},
author={Jerry Kazdan and Frank W. Warner},
journal={Annals of Mathematics},
year={1974},
volume={99},
pages={14}
}
• Published 1974
• Mathematics
• Annals of Mathematics
505 Citations
p-th Kazdan-Warner equation on graph
Let $G=(V,E)$ be a connected finite graph and $C(V)$ be the set of functions defined on $V$. Let $\Delta_p$ be the discrete $p$-Laplacian on $G$ with $p>1$ and $L=\Delta_p-k$, where $k\in C(V)$ is
Symplectic vortex equations for Kahler cones over Sasakian manifolds
We obtain a Hitchin-Kobayashi-type correspondence for symplectic vortex equations, with the target a Kahler cone over a compact Sasakian manifold. We show that the correspondence reduces to studying
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Geophysics and Stuart vortices on a sphere meet differential geometry
• L. Rudnicki
• Computer Science
Communications on Pure and Applied Analysis
• 2022
It is proved new existence criteria relevant for the non-linear elliptic PDE of the form M1 valid when ocean surface currents are modeled, as well as several previously known results valid when the parameter regime is changed.
Two solutions to Kazdan-Warner’s problem on surfaces
• Li Ma
• Mathematics
Proceedings of the American Mathematical Society
• 2021
In this paper, we study the sign-changing Kazdan-Warner's problem on two dimensional closed Riemannian manifold with negative Euler number $\chi(M)<0$. We show that once, the direct method on convex
Existence of Kazdan-Warner equation with sign-changing prescribed function
• Mathematics
• 2020
In this paper, we study the following Kazdan-Warner equation with sign-changing prescribed function h −∆u = 8π 

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