For Riemannian manifolds with a measure (M, g, e− f dvolg) we prove mean curvature and
volume comparison results when the∞-Bakry-Emery Ricci tensor is bounded from below …

We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces
with free boundary in a compact $ n $-dimensional Riemannian manifold which has …

The goal of the paper is four-fold. In the setting of non-smooth spaces with Ricci curvature
lower bounds (more precisely RCD (K, N) metric measure spaces):-we develop an intrinsic …

The goal of the paper is to give an optimal transport characterization of sectional curvature
lower (and upper) bounds for smooth n-dimensional Riemannian manifolds. More generally …

While it is well known from examples that no interesting “halfspace theorem” holds for
properly immersed-dimensional self-translating mean curvature flow solitons in Euclidean …

Positive k th-intermediate Ricci curvature on a Riemannian n-manifold, to be denoted by Ric
k> 0, is a condition that interpolates between positive sectional and positive Ricci curvature …

We prove splitting theorems for mean convex open subsets in Riemannian curvature-
dimension (RCD) spaces that extend results by Kasue et al. for Riemannian manifolds with …

We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently
separated at infinity must intersect at a finite point. The proof is based on a localized version …

We prove a rigidity theorem in the style of Urbano for the Allen-Cahn equation on the three-
sphere: the critical points with Morse index five are symmetric functions that vanish on a …

Let M be a compact Riemannian manifold of nonnegative Ricci curvature and† a compact
embedded 2-sided minimal hypersurface in M. It is proved that there is a dichotomy: If† does …