Cheng, Jih-Hsin, Hwang, Jenn-Fang, Malchiodi, A. and Yang, Paul (2012) A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. Journal fur die reine und angewandte Mathematik (Crelles Journal), Volume 2012 (Number 671). pp. 131-198. doi:10.1515/CRELLE.2011.159 ISSN 0075-4102.

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Abstract

In this paper, we study the structure of the singular set for a C1 smooth surface in the 3-dimensional Heisenberg group ℍ1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ1.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Journal fur die reine und angewandte Mathematik (Crelles Journal)
Publisher:	Walter de Gruyter GmbH & Co. KG
ISSN:	0075-4102
Official Date:	2012
Dates:	Date Event 2012 UNSPECIFIED
Volume:	Volume 2012
Number:	Number 671
Page Range:	pp. 131-198
DOI:	10.1515/CRELLE.2011.159
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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