Heintze--Karcher-Type Inequalities for the p-Laplacian and Serrin-Type Rigidity

@misc{soares2026heintzekarchertype,
  title = {{Heintze--Karcher-Type Inequalities for the $p$-Laplacian and Serrin-Type Rigidity}},
  author = {Matheus Nunes Soares and Weiller F. Chaves Barboza},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34252},
  eprint = {2609.34252},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34252},
}

TY  - UNPB
TI  - Heintze--Karcher-Type Inequalities for the p-Laplacian and Serrin-Type Rigidity
AU  - Matheus Nunes Soares
AU  - Weiller F. Chaves Barboza
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34252
UR  - https://arxiv.org/abs/2609.34252
AB  - We establish a parameterized Heintze--Karcher-type inequality for positive solutions of nonlinear Dirichlet problems involving the p-Laplacian, with p≥2, on bounded Riemannian domains. Under a Ricci curvature lower bound, positive boundary mean curvature, and suitable structural and approximation assumptions, the estimate follows from a regularized Reilly-type identity and a weighted Hessian inequality. We compare the resulting bound with previous estimates and investigate the geometry associated with equality. For p=2, an exact deficit identity allows the pointwise condition f'≤ nk to be replaced by a weighted integral condition. As applications, we obtain Heintze--Karcher and Soap Bubble-type rigidity results, with equality forcing the domain to be a metric ball and the solution to be radial.
ER  -