Heat content and horizontal mean curvature on the Heisenberg group
Heat content and horizontal mean curvature on the Heisenberg group
复制标题
海森堡群的热含量和水平平均曲率
DOI：
10.1080/03605302.2018.1446166
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发表时间：
2017
影响因子：
1.9
通讯作者：
Jing Wang
中科院分区：
文献类型：
--
作者：
J. Tyson;Jing Wang
摘要 我们确定了第一海森堡群中平滑有界域的亚黎曼热含量的短时渐近。我们的渐近公式将 van den Berg–Le Gall 和 van den Berg–Gilkey 的先前工作推广到亚黎曼环境，并根据水平周长和边界的总水平平均曲率确定了亚黎曼热含量的前几个系数。该证明是概率性的，并且依赖于布朗运动的热含量表征。
ABSTRACT We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van den Berg–Le Gall and van den Berg–Gilkey to the sub-Riemannian context, and identifies the first few coefficients in the sub-Riemannian heat content in terms of the horizontal perimeter and the total horizontal mean curvature of the boundary. The proof is probabilistic, and relies on a characterization of the heat content in terms of Brownian motion.