Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel

Braun, Mathias

doi:10.1016/j.jfa.2022.109599

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2024

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Cited by 3 publications

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“…Acknowledgment. The author would like to thank Professor Mathias Braun for notifying us the reference [13] after the first draft of this paper. His comment and advice helped us so much to improve the quality of this paper.…”

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confidence: 99%

Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian

Kuwae

Sakurai

2021

Illinois J. Math.

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The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and Tamanini [27] as a Dirichlet space having a weak form of Bakry-Émery curvature lower bounds in distribution sense. After their work, Braun [14] established a vector calculus for it, in particular, the space of L 2 -normed L ∞ -module describing vector fields, 1-forms, Hessian in L 2 -sense. In this framework, we establish the Hess-Schrader-Uhlenbrock inequality for 1-forms as an element of L 2 -cotangent module (an L 2 -normed L ∞ -module), which extends the Hess-Schrader-Uhlenbrock inequality by Braun [14] under an additional condition.

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confidence: 99%