Constructs a Morse theory for distance functions from definable sets to manifolds via Lipschitz critical points, with quadratic and PL indices, and applies it to bound critical points between generic algebraic hypersurfaces.
Curvature measures
3 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 3representative citing papers
A necessary and sufficient condition is proved for C¹-hypersurfaces whose parallel sets are all nowhere C¹-regular, implying the same for generic convex bodies.
Proves singular set estimates near boundaries for non-uniformly elliptic equations in higher co-dimension via a cone-based variant of quantitative stratification.
citing papers explorer
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Morse theory of Euclidean distance functions from algebraic hypersurfaces
Constructs a Morse theory for distance functions from definable sets to manifolds via Lipschitz critical points, with quadratic and PL indices, and applies it to bound critical points between generic algebraic hypersurfaces.
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When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular
A necessary and sufficient condition is proved for C¹-hypersurfaces whose parallel sets are all nowhere C¹-regular, implying the same for generic convex bodies.
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Singular set estimates for solutions to elliptic equations in higher co-dimension
Proves singular set estimates near boundaries for non-uniformly elliptic equations in higher co-dimension via a cone-based variant of quantitative stratification.