On the manifold of closed hypersurfaces in R^n
Jan Pruess, Gieri Simonett
TL;DR
This paper develops a set of differential geometry tools for analyzing the manifold of closed hypersurfaces in R^n, facilitating the study of moving interfaces and semiflow asymptotics.
Contribution
It introduces new differential geometry results tailored for the manifold of closed hypersurfaces, enhancing the direct mapping method for interface problems.
Findings
Provides a comprehensive differential geometry toolkit
Enables better analysis of moving interfaces
Aids in studying semiflow asymptotics
Abstract
Several results from differential geometry of hypersurfaces in R^n are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the asymptotics of the induced semiflows.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations