5 papers
Sobolev and Michael-Simon inequalities via the ABP method beyond Euclidean volume growth
Debora Impera, Michele Rimoldi, Giona Veronelli
We develop an ABP approach to Sobolev and Michael-Simon type inequalities under volume noncollapsing assumptions. The main new observation is a refinement of Brendle's contact-set…
Classification of quadratically pinched self-shrinkers in higher codimension
Debora Impera, Michele Rimoldi, Francesco Ruatta
We classify properly immersed self-shrinkers of the mean curvature flow in arbitrary codimension under a quadratic pinching condition of Andrews-Baker type on the second fundamenta…
Asymptotically non-negative Ricci curvature, elliptic Kato constant and isoperimetric inequalities
Debora Impera, Michele Rimoldi, Giona Veronelli
The ABP method for proving isoperimetric inequalities has been first employed by Cabré in , then developed by Brendle, notably in the context of non-compact Riemanni…
Rigidity and non-existence results for collapsed translators
Debora Impera, Niels Martin Møller, Michele Rimoldi
We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R…
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…