Density estimates for compact surfaces with total boundary curvature less than 4pi

TL;DR

This paper establishes density estimates for compact immersed surfaces in R^n with boundary curvature below 4pi and small mean curvature, extending previous results and exploring implications for their geometry and topology.

Contribution

It generalizes existing density estimates to broader classes of surfaces with boundary curvature less than 4pi and small mean curvature in L^p norm.

Findings

Density estimates for surfaces with boundary curvature less than 4pi

Extension of previous geometric results

Implications for surface topology and geometry

Abstract

In this paper we obtain density estimates for compact surfaces immersed in R^n with total boundary curvature less than 4pi and with sufficiently small L^p norm of the mean curvature, p>2. Our results generalize the main results in [2]. We then apply our estimates to discuss the geometry and topology of such surfaces.