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math.DG2026
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…
math.DG2025
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…
math.DG2025
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…