01095nas a2200145   4500008004100000022001400041245011100055210006900166260000800235300001400243490000700257520061900264100002000883856004600903       2014                        eng d  a1432-083500aExistence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds0 aExistence of integral mvarifolds minimizing int Ap and int Hp pm  cJan  a431–4700 v493 a<p>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 $(N,g)$, $2 \leq m&lt;n$ and $p&gt;m$ 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 $\int&nbsp; |H|^p$to&nbsp; avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.</p>1 aMondino, Andrea  uhttps://doi.org/10.1007/s00526-012-0588-y