19 citations · 85 across the 35 of their papers we have counts for
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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…
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…
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 Riemannia…
Density and non-density of on complete manifolds with curvature bounds
Shouhei Honda, Luciano Mari, Michele Rimoldi +1
We investigate the density of compactly supported smooth functions in the Sobolev space on complete Riemannian manifolds. In the first part of the paper, we extend to the…
Higher order distance-like functions and Sobolev spaces
Debora Impera, Michele Rimoldi, Giona Veronelli
We consider complete Riemannian manifolds with a controlled growth of the covariant derivatives of Ricci curvatures up to order and a controlled decay of the injectivity radi…
Density problems for second order Sobolev spaces and cut-off functions on manifolds with unbounded geometry
Debora Impera, Michele Rimoldi, Giona Veronelli
We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvatur…