Some functionals on compact manifolds with boundary
Pengzi Miao, Luen-Fai Tam
TL;DR
This paper investigates critical points of specific Riemannian metric functionals on compact manifolds with boundary, inspired by mass formulas in asymptotically flat and hyperbolic geometries, contributing to geometric analysis.
Contribution
It introduces new analysis of functionals related to mass in geometric settings, focusing on boundary effects and critical point characterization.
Findings
Identification of critical points for the functionals studied
Connections established between boundary geometry and mass functionals
Insights into geometric structures influencing mass formulas
Abstract
We analyze critical points of two functionals of Riemannian metrics on compact manifolds with boundary. These functionals are motivated by formulae of the mass functionals of asymptotically flat and asymptotically hyperbolic manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology