Boundary Curves of Free Boundary Minimal Surfaces
Zuhuan Yu
TL;DR
This paper proves that the intersection curves of free boundary minimal surfaces in the unit ball with the sphere are all circles, using holomorphic techniques to analyze their boundary behavior.
Contribution
It establishes a new geometric characterization of boundary curves of free boundary minimal surfaces in Euclidean 3-space.
Findings
All intersection curves with the sphere are circles.
Holomorphic methods effectively analyze free boundary minimal surfaces.
Provides a geometric classification of boundary curves.
Abstract
In this paper we investigate free boundary minimal surfaces in the unit ball in Euclidean 3-space, and by using holomorphic techniques we prove that intersection curves of free boundary minimal surfaces with the unit sphere are all circles.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Analytic and geometric function theory