The affine Plateau problem
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- by Neil S. Trudinger and Xu-Jia Wang;
- J. Amer. Math. Soc. 18 (2005), 253-289
- DOI: https://doi.org/10.1090/S0894-0347-05-00475-3
- Published electronically: January 3, 2005
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Abstract:
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.References
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Bibliographic Information
- Neil S. Trudinger
- Affiliation: Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia
- Email: Neil.Trudinger@maths.anu.edu.au
- Xu-Jia Wang
- Affiliation: Centre for Mathematics and Its Applications, Australian National University, Canberra, ACT 0200, Australia
- Email: X.J.Wang@maths.anu.edu.au
- Received by editor(s): September 3, 2003
- Published electronically: January 3, 2005
- Additional Notes: This research was supported by the Australian Research Council
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 18 (2005), 253-289
- MSC (2000): Primary 35J40; Secondary 53A15
- DOI: https://doi.org/10.1090/S0894-0347-05-00475-3
- MathSciNet review: 2137978