Heudson Mirandola

THE NON-PARABOLICITY OF INFINITE VOLUME ENDS

Let M m , with m � 3, be an m-dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold ¯ M. Assume that the mean curvature vector has finite L p -norm, for some 2 � pm. We prove that each end of M must either have finite volume or be non-parabolic.

Homotopy groups, focal points, and totally geodesic immersions

In this paper we consider on a complete Riemannian manifold

L 2 -HARMONIC 1-FORMS ON SUBMANIFOLDS WITH FINITE TOTAL CURVATURE

M

The positive mass theorem and Penrose inequality for graphical manifolds

an immersed totally geodesic hypersurface

Rigidity Theorems of conformal class on compact manifolds with boundary

\Si

Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces

existing together with an immersed submanifold

Global isometric embeddings of multiple warped product metrics into quadrics

N

Rigidity theorems on conformal class of compact manifolds with boundary

without focal points. No curvature condition is needed. We obtained several connectedness results relating the topologies of

Multiple warped product metrics into quadrics

M

Hardy and Rellich inequalities for submanifolds in Hadamard spaces

and