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PreprintarXiv licencearXiv

Mixed Radial Volume Comparison under Spectral Ricci Bounds

  • Han Hong
  • Gaoming Wang
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Abstract

Let (Mn,g) be complete, let u>0, and assume Ricg−α(Δg u)/ug≥ (n−1)κg. We introduce mixed radial balls associated with the conformal metric u2αg. For these mixed radial balls, we obtain a space-form-sharp model comparison and polynomial weighted volume growth without pointwise bounds on u. As applications, we give a radial derivation of the spectral Bonnet--Myers and sharp volume theorem of Antonelli--Xu, and a short volume growth derivation of the stable Bernstein theorem in ℝ4.

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Cite

BibTeXRIS
BibTeX
@misc{hong2026mixed,
  title = {{Mixed Radial Volume Comparison under Spectral Ricci Bounds}},
  author = {Han Hong and Gaoming Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02430},
  eprint = {2609.02430},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02430},
}
RIS
TY  - UNPB
TI  - Mixed Radial Volume Comparison under Spectral Ricci Bounds
AU  - Han Hong
AU  - Gaoming Wang
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02430
UR  - https://arxiv.org/abs/2609.02430
AB  - Let (M^n,g) be complete, let u>0, and assume Ric_g−α(Δ_g u)/ug≥ (n−1)κg. We introduce mixed radial balls associated with the conformal metric u^2αg. For these mixed radial balls, we obtain a space-form-sharp model comparison and polynomial weighted volume growth without pointwise bounds on u. As applications, we give a radial derivation of the spectral Bonnet--Myers and sharp volume theorem of Antonelli--Xu, and a short volume growth derivation of the stable Bernstein theorem in ℝ^4.
ER  -