Uniform doubling for abelian products with $\operatorname{SU}(2)$

Nathaniel Eldredge; Maria Gordina; Laurent Saloff-Coste

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arXiv · 2412.17102

Uniform doubling for abelian products with $\operatorname{SU}(2)$

Nathaniel Eldredge·Maria Gordina·Laurent Saloff-Coste

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Abstract

We prove that the uniform doubling property holds for every Lie group which can be written as a quotient group of $\operatorname{SU}(2) \times \mathbb{R}^n$ for some $n$. In particular, this class includes the four-dimensional unitary group $\operatorname{U}(2)$. As this class contain non-compact as well as compact Lie groups, we discuss a number of analytic and spectral consequences for the corresponding heat kernels.

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Nathaniel Eldredge, Maria Gordina, Laurent Saloff-Coste. 2024-12-22. Uniform doubling for abelian products with $\operatorname{SU}(2)$. https://arxiv.org/abs/2412.17102

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