Boundary value problems for metrics on 3-manifolds
Michael T. Anderson
TL;DR
This paper investigates the mathematical problem of prescribing boundary data such as mean curvature and conformal class for Einstein metrics on 3-manifolds, focusing on elliptic boundary value problems in Riemannian geometry.
Contribution
It introduces a framework for boundary value problems involving Einstein metrics on 3-manifolds with prescribed boundary data.
Findings
Formulation of elliptic boundary value problems for Einstein metrics
Analysis of conditions for existence and uniqueness of solutions
Insights into geometric structures of 3-manifolds with prescribed boundary data
Abstract
We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Holomorphic and Operator Theory