Title | Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds |
Publication Type | Journal Article |
Year of Publication | 2014 |
Authors | Mondino, A |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 49 |
Pagination | 431–470 |
Date Published | Jan |
ISSN | 1432-0835 |
Abstract | We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals. |
URL | https://doi.org/10.1007/s00526-012-0588-y |
DOI | 10.1007/s00526-012-0588-y |
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