Refines Brendle's ABP contact-set argument to prove Michael-Simon inequalities with lower-order terms for submanifolds in nonnegative-curvature manifolds under volume noncollapsing, plus an ABP proof of Varopoulos' L1-Sobolev inequality.
A mass-transportation ap- proach to sharp Sobolev and Gagliardo-Nirenberg inequalities
2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.
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Sobolev and Michael-Simon inequalities via the ABP method beyond Euclidean volume growth
Refines Brendle's ABP contact-set argument to prove Michael-Simon inequalities with lower-order terms for submanifolds in nonnegative-curvature manifolds under volume noncollapsing, plus an ABP proof of Varopoulos' L1-Sobolev inequality.
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Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.