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Spectral Γ2 inequalities for the V-Laplacian with evolving weighted measures

  • Ha Tuan Dung
  • Yi Li
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Abstract

In this paper, we establish spectral Bakry-Émery Γ2 criteria and their modified counterparts for the V-Laplacian on closed Riemannian manifolds equipped with evolving weighted measures. The estimates yield jointly optimized spectral bounds and sharp endpoint constants. When the measures evolve according to the Fokker-Planck equation, these estimates yield monotonicity formulas for the Fisher information associated with Shannon and Tsallis entropies, together with quantitative propagation of Poincaré, logarithmic Sobolev, and nonlinear interpolation inequalities. In the stationary reversible setting, our results specialize to the Witten Laplacian and recover the unweighted Cai-Wang estimates \cite{Cai}.

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Cite

BibTeXRIS
BibTeX
@misc{dung2026spectral,
  title = {{Spectral $Γ_2$ inequalities for the $V$-Laplacian with evolving weighted measures}},
  author = {Ha Tuan Dung and Yi Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36091},
  eprint = {2610.36091},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36091},
}
RIS
TY  - UNPB
TI  - Spectral Γ_2 inequalities for the V-Laplacian with evolving weighted measures
AU  - Ha Tuan Dung
AU  - Yi Li
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36091
UR  - https://arxiv.org/abs/2610.36091
AB  - In this paper, we establish spectral Bakry-Émery Γ_2 criteria and their modified counterparts for the V-Laplacian on closed Riemannian manifolds equipped with evolving weighted measures. The estimates yield jointly optimized spectral bounds and sharp endpoint constants. When the measures evolve according to the Fokker-Planck equation, these estimates yield monotonicity formulas for the Fisher information associated with Shannon and Tsallis entropies, together with quantitative propagation of Poincaré, logarithmic Sobolev, and nonlinear interpolation inequalities. In the stationary reversible setting, our results specialize to the Witten Laplacian and recover the unweighted Cai-Wang estimates \cite{Cai}.
ER  -