On mean-convex Alexandrov embedded surfaces in the 3-sphere

TL;DR

This paper investigates conditions under which mean-convex Alexandrov embedded surfaces in the 3-sphere can be continuously deformed while maintaining their embeddedness and mean-convexity.

Contribution

It provides new criteria for deforming such surfaces in the 3-sphere without losing their geometric properties.

Findings

Identified conditions for continuous deformation preserving embeddedness.

Established criteria for maintaining mean-convexity during deformation.

Contributed to understanding the geometric behavior of surfaces in the 3-sphere.

Abstract

We consider mean-convex Alexandrov embedded surfaces in the round unit 3-sphere, and show under which conditions it is possible to continuously deform these preserving mean-convex Alexandrov embeddedness.