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A new characterization of the round sphere
Abstract
We provide an elementary proof of Hersch's inequality and Cheng's theorem, both characterizing the sphere. We revisit these classical results in connection with the geodesic monotonicity of heat kernels on two-dimensional spheres, which provides a third characterization.
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BibTeX
@misc{burchard2026characterization,
title = {{A new characterization of the round sphere}},
author = {Almut Burchard and Ángel D. Martínez},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08751},
eprint = {2611.08751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08751},
}
RIS
TY - UNPB
TI - A new characterization of the round sphere
AU - Almut Burchard
AU - Ángel D. Martínez
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08751
UR - https://arxiv.org/abs/2611.08751
AB - We provide an elementary proof of Hersch's inequality and Cheng's theorem, both characterizing the sphere. We revisit these classical results in connection with the geodesic monotonicity of heat kernels on two-dimensional spheres, which provides a third characterization.
ER -