A maximum principle for free boundary minimal varieties of arbitrary codimension
Martin Li, Xin Zhou
TL;DR
This paper proves a maximum principle for free boundary minimal submanifolds of any dimension and codimension within Riemannian manifolds, extending to varifolds.
Contribution
It introduces a boundary maximum principle applicable to free boundary minimal varieties of arbitrary codimension, broadening previous results.
Findings
Maximum principle valid for all dimensions and codimensions
Applicable to varifolds, not just smooth submanifolds
Enhances understanding of boundary behavior of minimal varieties
Abstract
We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds