We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in
has intrinsic cubic volume growth, provided the parametric elliptic integral is-close to the …

This book describes very recent results involving an extensive use of analytical tools in the
study of geometrical and topological properties of complete Riemannian manifolds. It …

Calculus of Variations Page 1 Calc. Var. (2007) 29:281–293 DOI 10.1007/s00526-006-0033-1
Calculus of Variations Stability of translating solutions to mean curvature flow Julie Clutterbuck …

In this paper, we studied complete manifolds whose spectrum of the Laplacian has a
positive lower bound. In particular, if the Ricci curvature is bounded from below by some …

The aim of this paper is to prove two results concerning the rigidity of complete, immersed,
orientable, stable minimal hypersurfaces: we show that they are hyperplane in R 4, while …

Function theory on Euclidean domains in relation to potential theory, partial differential
equations, probability, and harmonic analysis has been the target of investigation for …

We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower
bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the …

Let M be a smooth Riemannian manifold that is the union of a compact part and a finite
number of Euclidean ends, R n∖ B (0, R) for some R> 0, each of which carries the standard …

We prove that finite Morse index solutions to the Allen‐Cahn equation in ℝ2 have finitely
many ends and linear energy growth. The main tool is a curvature decay estimate on level …

Let M be an n-dimensional complete non-compact submanifold in a hyperbolic space with
the norm of its mean curvature vector bounded by a constant α<n-1. We prove in this paper …