C-1,C-alpha-regularity for surfaces with H is an element of L-p

Theodora Bourni, Giuseppe Tinaglia*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we prove several results on the geometry of surfaces immersed in with small or bounded norm of . For instance, we prove that if the norm of and the norm of , , are sufficiently small, then such a surface is graphical away from its boundary. We also prove that given an embedded disk with bounded norm of , not necessarily small, then such a disk is graphical away from its boundary, provided that the norm of is sufficiently small, . These results are related to previous work of Schoen-Simon (Surfaces with quasiconformal Gauss map. Princeton University Press, Princeton, vol 103, pp 127-146, 1983) and Colding-Minicozzi (Ann Math 160:69-92, 2004).

Original languageEnglish
Pages (from-to)159-186
Number of pages28
JournalANNALS OF GLOBAL ANALYSIS AND GEOMETRY
Volume46
Issue number2
DOIs
Publication statusPublished - Aug 2014

Keywords

  • CURVATURE
  • SPACE

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