76 citations · 133 across the 35 of their papers we have counts for
27 papers · 1 filter
Lower bounds on the normal injectivity radius of hypersurfaces and bounded geometries on manifolds with boundary
Sebastian Boldt, Batu Güneysu, Stefano Pigola
We prove for the first time a pointwise lower estimate of the normal injectivity radius of an embedded hypersurface in an arbitrary Riemannian manifold. Main applications include:…
Isoperimetric and Michael-Simon inequalities on manifolds with asymptotically nonnegative curvature
Debora Impera, Stefano Pigola, Michele Rimoldi +1
We establish the validity of the isoperimetric inequality (or equivalently, an Euclidean-type Sobolev inequality) on manifolds with asymptotically non-negative sectional curv…
The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's
Debora Impera, Stefano Pigola, Michele Rimoldi
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…
Nonlinear Calderón-Zygmund inequalities for maps
Batu Güneysu, Stefano Pigola
Being motivated by the problem of deducing -bounds on the second fundamental form of an isometric immersion from -bounds on its mean curvature vector field, we prove a (n…
Height estimates for Killing graphs
Debora Impera, Jorge H. de Lira, Stefano Pigola +1
The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric anal…
Dirichlet parabolicity and -Liouville property under localized geometric conditions
Leandro F. Pessoa, Stefano Pigola, Alberto G. Setti
We shed a new light on the -Liouville property for positive, superharmonic functions by providing many evidences that its validity relies on geometric conditions localized on…