Refinement of Brendle's contact-set argument enables ABP proofs of Michael-Simon and Varopoulos-type Sobolev inequalities with lower-order terms under volume noncollapsing on manifolds with nonnegative sectional curvature.
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Sobolev and Michael-Simon inequalities via the ABP method beyond Euclidean volume growth
Refinement of Brendle's contact-set argument enables ABP proofs of Michael-Simon and Varopoulos-type Sobolev inequalities with lower-order terms under volume noncollapsing on manifolds with nonnegative sectional curvature.