Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry

2024/05/23 by Stefan Ivanov, Ivanov, Stefan, Alexander Petkov +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2405.14845

openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish in the present paper two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension 4n+3, provided some positivity conditions are satisfied. These are qc versions of the prominent Li-Yau gradient estimate in Riemannian geometry. Another goal of this paper is to get two Perelman-type entropy formulas for the qc heat equation on a compact qc-Einstein manifold of dimension 4n+3 with non-negative qc scalar curvature (e.g. compact 3-Sasakian manifold), as well as an integral sub-gradient estimate for the positive solutions of the qc heat equation.

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