2010 / December Volume 5 No.4
Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group
| Published Date |
2010 / December
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|---|---|
| Title | Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group |
| Author | |
| Keyword | |
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| Pagination | 369-412 |
| Abstract | We prove the existence of a continuous $BV$ minimizer with $C^{0}$
boundary value for the $p$-area (pseudohermitian or horizontal area)
in a parabolically convex bounded domain. We extend the domain of
the area functional from $BV$ functions to vector-valued measures.
Our main purpose is to study the first and second variations of such
a generalized area functional including the contribution of the
singular part. By giving examples in Riemannian and pseudohermitian
geometries, we illustrate several known results in a unified way. We
show the contribution of the singular curve in the first and second
variations of the $p$-area for a surface in an arbitrary
pseudohermitian $3$-manifold.
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| AMS Subject Classification |
35L80, 35J70, 32V20, 53A10, 49Q10
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| Received |
2010-12-08
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| Accepted |
2010-12-28
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