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PreprintarXiv licencearXiv

Almgren frequency and Agmon convexity on rotationally symmetric Cartan-Hadamard manifolds

  • Luca F. Di Cerbo
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Abstract

We introduce a \emph{global} frequency function for harmonic functions on rotationally symmetric Cartan-Hadamard manifolds. In real hyperbolic space, we also identify a different frequency function associated with the normalized spherical L2-mass of a hyperbolic harmonic function and prove its monotonicity. As a consequence, we obtain a logarithmic convexity theorem for the normalized spherical L2-mass and a hyperbolic analog of the classical three-sphere theorem.

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Cite

BibTeXRIS
BibTeX
@misc{cerbo2026almgren,
  title = {{Almgren frequency and Agmon convexity on rotationally symmetric Cartan-Hadamard manifolds}},
  author = {Luca F. Di Cerbo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03549},
  eprint = {2610.03549},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03549},
}
RIS
TY  - UNPB
TI  - Almgren frequency and Agmon convexity on rotationally symmetric Cartan-Hadamard manifolds
AU  - Luca F. Di Cerbo
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03549
UR  - https://arxiv.org/abs/2610.03549
AB  - We introduce a \emph{global} frequency function for harmonic functions on rotationally symmetric Cartan-Hadamard manifolds. In real hyperbolic space, we also identify a different frequency function associated with the normalized spherical L^2-mass of a hyperbolic harmonic function and prove its monotonicity. As a consequence, we obtain a logarithmic convexity theorem for the normalized spherical L^2-mass and a hyperbolic analog of the classical three-sphere theorem.
ER  -