Spheres of prescribed mean curvature in S^3

TL;DR

This paper establishes conditions for the existence of conformal embeddings of the two-sphere into the three-sphere with a specified mean curvature, advancing understanding of geometric embeddings in spherical spaces.

Contribution

It provides a semi-global existence result for conformal embeddings with prescribed mean curvature in the three-sphere, a novel contribution to geometric analysis.

Findings

Existence of conformal embeddings with prescribed mean curvature

Semi-global result applicable to S^3

Advances in geometric embedding theory

Abstract

We prove a semi-global result on the existence of conformal embeddings of the two-sphere into the round three-sphere S^3(1) with prescribed mean curvature.