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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2012, Issue 671

Issues

A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group

Jih-Hsin Cheng
  • Institute of Mathematics, Academia Sinica, Taipei 11529
  • National Center for Theoretical Sciences, Taipei Office, Taiwan, R.O.C.
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/ Jenn-Fang Hwang
  • Institute of Mathematics, Academia Sinica, Taipei 11529
  • National Center for Theoretical Sciences, Taipei Office, Taiwan, R.O.C.
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/ Andrea Malchiodi / Paul Yang
Published Online: 2011-10-24 | DOI: https://doi.org/10.1515/CRELLE.2011.159

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.

About the article

Received: 2010-06-18

Revised: 2011-04-07

Published Online: 2011-10-24

Published in Print: 2012-10-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 671, Pages 131–198, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.159.

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Citing Articles

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[1]
Jih-Hsin Cheng and Jenn-Fang Hwang
Calculus of Variations and Partial Differential Equations, 2014, Volume 50, Number 3-4, Page 579
[2]
Luca Capogna and Giovanna Citti
Bulletin of Mathematical Sciences, 2016, Volume 6, Number 2, Page 173
[3]
Matteo Galli
Pacific Journal of Mathematics, 2014, Volume 271, Number 1, Page 143

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