In this paper we consider complete noncompact Riemannian manifolds (M, g) with
nonnegative Ricci curvature and Euclidean volume growth, of dimension n ≥ 3 n≥ 3. For …

In this paper, we prove an extended version of the Minkowski Inequality, holding for any
smooth bounded set Ω⊂ R n, n≥ 3. Our proof relies on the discovery of effective …

On the Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space
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We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in
hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals …

We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in
warped product manifolds with a positive warping factor ϕ (r) ϕ (r). If ϕ'(r)> 0 ϕ′(r)> 0 and …

In this article, we will use inverse mean curvature flow to establish an optimal Sobolev-type
inequality for hypersurfaces Σ Σ with nonnegative sectional curvature in H^ n H n. As an …

We prove that a proper weak solution $\{\Omega_ {t}\} _ {0\leq t<\infty} $ to inverse mean
curvature flow in $\mathbb {H}^{n} $, $3\leq n\leq 7$, is smooth and star-shaped by the …

The long-time existence and umbilicity estimates for compact, graphical solutions to
expanding curvature flows are deduced in Riemannian warped products of a real interval …

We prove convergence results for expanding curvature flows in the Euclidean and
hyperbolic space. The flow speeds have the form, where and F is a positive, strictly …

We study the evolution of complete, noncompact, convex hypersurfaces in R n+ 1 by the
inverse mean curvature flow. We establish the long-time existence of solutions, and we …