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Spectral Improvements of Geometric Inequalities on Closed Kähler Manifolds

  • Sayantan Chakraborty
  • Xiaodong Wang
  • Tian Wu
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Abstract

Let (M,g,J) be a closed Kähler manifold satisfying Ricgeqslant g. We establish improved Liouville theorems for the Euler--Lagrange equations associated with the Beckner--Sobolev inequalities by incorporating the first positive eigenvalue of the ∂̅-Laplacian into a differential-identity argument. As a consequence, we obtain improved Sobolev and Beckner inequalities that refine the known Riemannian and Kähler estimates when the first eigenvalue is sufficiently large. We also derive new upper bounds for the diameter of (M,g).

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Cite

BibTeXRIS
BibTeX
@misc{chakraborty2026spectral,
  title = {{Spectral Improvements of Geometric Inequalities on Closed Kähler Manifolds}},
  author = {Sayantan Chakraborty and Xiaodong Wang and Tian Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03287},
  eprint = {2609.03287},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03287},
}
RIS
TY  - UNPB
TI  - Spectral Improvements of Geometric Inequalities on Closed Kähler Manifolds
AU  - Sayantan Chakraborty
AU  - Xiaodong Wang
AU  - Tian Wu
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03287
UR  - https://arxiv.org/abs/2609.03287
AB  - Let (M,g,J) be a closed Kähler manifold satisfying Ricgeqslant g. We establish improved Liouville theorems for the Euler--Lagrange equations associated with the Beckner--Sobolev inequalities by incorporating the first positive eigenvalue of the ∂̅-Laplacian into a differential-identity argument. As a consequence, we obtain improved Sobolev and Beckner inequalities that refine the known Riemannian and Kähler estimates when the first eigenvalue is sufficiently large. We also derive new upper bounds for the diameter of (M,g).
ER  -