Minimizers of the Willmore functional under fixed conformal class
By Ernst Kuwert, R. Schatzle. 2010
60 citations recorded by the source corpus.
We consider the problem of minimizing the Willmore energy in the class of conformal immersions of a given closed, genus p Riemann surface into R^n for n=3,4. We prove existence of a smooth minimizer, provided that the infimum is below a certain bound ${\cal W}(n,p)$. For tori in R^3 we have explicitely ${\cal W}(3,1) = 8\pi$.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/4abf7f7d148a6edb112c36298103019e4e7d06a6
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data (2010, background): “We want to mention in particular BauerKuwert and Simon [1, 27] for existence of closed Willmore surfaces of prescribed genus, Kuwert–Schätzle and Leschke–Pedit–Pinkall [17,18,21] for constrained closed Willmore surfaces of fixed conformal class and Rivière [25] for a far reaching regularity result.”