The prescribed scalar curvature problem for metrics with unit total volume
Shinichiroh Matsuo
TL;DR
This paper addresses the problem of finding Riemannian metrics with a specified scalar curvature while maintaining a fixed total volume, solving a modified version of the Kazdan-Warner problem.
Contribution
It introduces a solution to the modified Kazdan-Warner problem for metrics with prescribed scalar curvature and fixed total volume.
Findings
Successfully solves the modified Kazdan-Warner problem.
Provides conditions for existence of metrics with prescribed scalar curvature.
Advances understanding of scalar curvature prescription under volume constraints.
Abstract
We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Geometry and complex manifolds