The paper proves a Fenchel-Willmore-Chen inequality for submanifolds in smooth metric measure spaces with lower bounds on the 1-Bakry-Emery n-Ricci curvature, plus Sobolev and isoperimetric inequalities under nonnegative 1-weighted Ricci curvature.
Sobolev Inequality In Manifolds With Lower Quadratic Curvature Decay
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abstract
By using the ABP method developed by Cabr\'e and Brendle, we establish some Sobolev inequalities for compact domains and submanifolds in a complete Riemannian manifold with lower quadratic curvature decay
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Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature
The paper proves a Fenchel-Willmore-Chen inequality for submanifolds in smooth metric measure spaces with lower bounds on the 1-Bakry-Emery n-Ricci curvature, plus Sobolev and isoperimetric inequalities under nonnegative 1-weighted Ricci curvature.