Related papers: Remark on a geometric inequality for closed hypers…
In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in weighted manifolds with nonnegative Bakry-\'Emery Ricci curvature. In particular, we give a sharp Willmore type inequality in steady gradient Ricci…
In this paper we consider complete noncompact Riemannian manifolds $(M, g)$ with nonnegative Ricci curvature and Euclidean volume growth, of dimension $n \geq 3$. We prove a sharp Willmore-type inequality for closed hypersurfaces $\partial…
There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the…
In this work we establish a sharp geometric inequality for closed hypersurfaces in complete noncompact Riemannian manifolds with asymptotically nonnegative curvature using standard comparison methods in Riemannian Geometry. These methods…
For Riemannian manifolds with a measure $(M,g, e^{-f} dvol_g)$ we prove mean curvature and volume comparison results when the $\infty$-Bakry-Emery Ricci tensor is bounded from below and $f$ is bounded or $\partial_r f$ is bounded from…
We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the…
We prove that if $(X,\mathsf{d},\mathfrak{m})$ is a metric measure space with $\mathfrak{m}(X)=1$ having (in a synthetic sense) Ricci curvature bounded from below by $K>0$ and dimension bounded above by $N\in [1,\infty)$, then the classic…
In this paper, we study stable weighted minimal hypersurfaces in manifolds with nonnegative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of…
Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n$, for $3 \leq n \leq 7$, and non-negative Ricci curvature. Let $g = \phi^2 g_0$ be a metric in the conformal class of $g_0$. We show that there exists a smooth closed embedded…
In this paper we prove that on a complete smooth metric measure space with non-negative Bakry-\'Emery-Ricci curvature if the space of weighted L^2 harmonic one-forms is non-trivial then the weighted volume of the manifold is finite and…
In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when $\infty$-dimensional Bakry-\'Emery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted…
We give a simple proof of a recent result due to Agostiniani, Fogagnolo and Mazzieri.
The sharp isoperimetric inequality for non-compact Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth has been obtained in increasing generality with different approaches in a number of contributions…
In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with ${\rm Ric}\geq-ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to…
The paper is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in…
We consider Riemannian manifolds $M_i$, ${i=0,1}$, with boundary and $\Phi_i\in C^{\infty}(M_i)$ non-negative such that the pair $(M_i, \Phi_i)$ admits Bakry-Emery $N$-Ricci curvature bounded from below by $K$. Let $Y_0$ and $Y_1$ be…
We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-\'Emery Ricci curvature. Our main goal is to classify positive solutions of the equation at the Sobolev-critical exponent,…
We extend the celebrated rigidity of the sharp first spectral gap under $Ric\ge0$ to compact infinitesimally Hilbertian spaces with non-negative (weak, also called synthetic) Ricci curvature and bounded (synthetic) dimension i.e. to…
In this note we extend a recent result of S. Brendle [3] to Riemannian manifolds with densities and nonnegative Bakry-\'Emery Ricci curvature.
We study both function theoretic and spectral properties on complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with nonnegative Bakry-\'{E}mery Ricci curvature. Among other things, we derive a gradient estimate for positive…