A Codazzi-like equation and the singular set for C-1 smooth surfaces in the Heisenberg group

Cheng, J; Hwang, J; Malchiodi, Andrea; Yang, P.

doi:10.1515/CRELLE.2011.159

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 di¤erential 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 that Codazzi-like equation by proving a fundamental theorem for local surfaces in H1

Titolo:	A Codazzi-like equation and the singular set for C-1 smooth surfaces in the Heisenberg group
Autori:	Cheng J Hwang J MALCHIODI, ANDREA Yang P. mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2012
Rivista:	JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK
Digital Object Identifier (DOI):	http://dx.doi.org/10.1515/CRELLE.2011.159
Handle:	http://hdl.handle.net/1234/56061
Appare nelle tipologie:	1.1 Articolo in rivista

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http://hdl.handle.net/11384/56061

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