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PDE methods for extracting normal vector fields and distance functions of shapes

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arxiv 2506.19323 v1 pith:YIGJZYEJ submitted 2025-06-24 math.AP math.OC

Takahiro Hasebe , Jun Masamune , Hiroshi Teramoto , Takayuki Yamada This is my paper · ORCID
classification math.APmath.OC
keywords equationdistanceellipticextractextractingmethodsnormalshapes
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Partial differential equations can be used for extracting geometric features of shapes. This article summarizes recent methods to extract the normal vector field from an elliptic equation proposed by Yamada and from the heat equation, and also a method to extract the (signed) distance function from an elliptic equation that generalizes Varadhan's in 1967.

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  1. Short-time behavior and invariant surfaces for caloric functions with non-constant boundary values

    math.AP 2026-07 conditional novelty 6.0 of 10

    For heat equations with zero initial data and non-negative Dirichlet data, short-time exponential decay is governed by the distance to the set where the boundary data is positive.

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