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.
Free boundary minimal surfaces with connected boundary and arbi- trary genus
5 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 5representative citing papers
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
Establishes a general min-max theorem producing minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature.
Heat semigroup characterizes total variation for compactly supported BV on arbitrary smooth complete weighted Riemannian manifolds, with a counterexample on some weighted manifold.
New proof that integer rectifiable currents with finite mass boundaries are integral, deduced from De Giorgi's BV theorem using cylindrical projections; also yields new compactness proof for integral currents.
citing papers explorer
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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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Self-Reconstructing Codazzi Defects, $\mathbb{CP}^1$ Quantization, and the Minimal Standard-Model Carrier
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
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Min-max theory and minimal surfaces with prescribed genus
Establishes a general min-max theorem producing minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature.
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Sets of finite perimeter on Riemannian manifolds and stochastic completeness
Heat semigroup characterizes total variation for compactly supported BV on arbitrary smooth complete weighted Riemannian manifolds, with a counterexample on some weighted manifold.
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Boundary rectifiability and compactness of integral currents via $BV$ functions
New proof that integer rectifiable currents with finite mass boundaries are integral, deduced from De Giorgi's BV theorem using cylindrical projections; also yields new compactness proof for integral currents.