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

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

2011-05-10

arxiv.org/abs/1105.1972v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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