Instituto Nacional de Matemática Pura e Aplicada

A Generalization of Marstrand’s Theorem and Some Geometric Applications

Abstract In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand’s projection theorem in a quite general formulation over metric spaces under a suitable transversality condition (the “projections" are in princip...

Existence of minimal surfaces in infinite-volume hyperbolic 3-manifolds

Abstract The existence of embedded minimal surfaces in non-compact 3-manifolds remains a largely unresolved and challenging problem in geometry. In this paper, we address several open cases regarding the existence of finite-area, embedded, complete, minimal surfaces in infinite-v...