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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math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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
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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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.