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The Sunada method on Metric Measure Spaces

  • Lewis Tadman
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Abstract

In this paper, we provide a general Sunada--Pesce--Sutton-type method that produces pairs of isospectral metric measure spaces. This construction relies on a representation theoretic assumption, and we give examples of spaces satisfying this condition, such as RCD spaces. As an application, we construct a pair of simply connected isospectral, non-isometric RCD non-Alexandrov spaces and a pair of Alexandrov non-orbifold spaces.

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Cite

BibTeXRIS
BibTeX
@misc{tadman2026sunada,
  title = {{The Sunada method on Metric Measure Spaces}},
  author = {Lewis Tadman},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28562},
  eprint = {2608.28562},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28562},
}
RIS
TY  - UNPB
TI  - The Sunada method on Metric Measure Spaces
AU  - Lewis Tadman
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28562
UR  - https://arxiv.org/abs/2608.28562
AB  - In this paper, we provide a general Sunada--Pesce--Sutton-type method that produces pairs of isospectral metric measure spaces. This construction relies on a representation theoretic assumption, and we give examples of spaces satisfying this condition, such as RCD spaces. As an application, we construct a pair of simply connected isospectral, non-isometric RCD non-Alexandrov spaces and a pair of Alexandrov non-orbifold spaces.
ER  -