Free boundary minimal surfaces with connected boundary and arbitrary genus
Alessandro Carlotto, Giada Franz, Mario B. Schulz
TL;DR
This paper demonstrates, using min-max methods, the existence of embedded free boundary minimal surfaces with connected boundary and any genus within the unit ball in three-dimensional space.
Contribution
It introduces a novel application of min-max techniques to construct free boundary minimal surfaces of arbitrary genus with connected boundary.
Findings
Existence of embedded free boundary minimal surfaces with arbitrary genus.
Construction within the unit ball in -dimensional space.
Application of min-max methods to free boundary problems.
Abstract
We employ min-max techniques to show that the unit ball in contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Point processes and geometric inequalities