Yamabe Equation on Some Complete Noncompact Manifolds
Guodong Wei
TL;DR
This paper investigates the Yamabe equation on complete noncompact Riemannian manifolds, establishing geometric conditions under which bounded positive solutions exist, advancing understanding of geometric analysis on such manifolds.
Contribution
It identifies specific geometric conditions that guarantee the existence of bounded positive solutions to the Yamabe problem on noncompact manifolds.
Findings
Established geometric conditions for solutions
Proved existence of bounded positive solutions
Extended Yamabe problem results to noncompact settings
Abstract
In this paper, we consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows