管状邻域上Heat Equations的L2-Homogenization
L2-Homogenization of Heat Equations on Tubular Neighborhoods
摘要：
本文考虑了闭黎曼子流形的管状邻域上具有Dirichlet边界条件的热方程。我们表明，作为管半径减小，半群的适当重新缩放和重整化的生成器可以有效地描述的哈密顿量的子流形上的潜在的，取决于几何形状的子流形和嵌入。
英文摘要：
We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can be effectively described by a Hamiltonian on the submanifold with a potential that depends on the geometry of the submanifold and of the embedding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
