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A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
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Jih-Hsin Cheng
,
Jenn-Fang Hwang
Published/Copyright:
October 24, 2011
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.
Received: 2010-06-18
Revised: 2011-04-07
Published Online: 2011-10-24
Published in Print: 2012-10
©[2012] by Walter de Gruyter Berlin Boston
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- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
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Articles in the same Issue
- Conformal maps from a 2-torus to the 4-sphere
- Sofic random processes
- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
- A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
- Spin representations of Weyl groups and the Springer correspondence
- Higgs bundles over the good reduction of a quaternionic Shimura curve
