Optimal bounds for ancient caloric functions

DOI10.1215/00127094-2021-0015zbMath1493.53055arXiv1902.01736OpenAlexW3217677520MaRDI QIDQ2073287

Tobias Holck Colding, William P. II. Minicozzi

Publication date: 1 February 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01736

zbMATH Keywords

polynomial volume growthoptimal boundscaloric functionsharmonic functions.Yau's 1974 conjecture

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Geometric evolution equations (53E99)

Related Items (9)

Complexity of parabolic systems ⋮ Polynomial growth ancient solutions to harmonic form heat flow ⋮ Rough hypoellipticity for the heat equation in Dirichlet spaces ⋮ Liouville theorems for ancient solutions to the \(V\)-harmonic map heat flows ⋮ Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons ⋮ Evolution of form and shape ⋮ Time regularity for local weak solutions of the heat equation on local Dirichlet spaces ⋮ A note on parabolic frequency and a theorem of Hardy–Pólya–Szegö ⋮ Ancient caloric functions on Pseudohermitian manifolds

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