Nonnegative solutions of the heat equation on rotationally symmetric Riemannian manifolds and semismall perturbations

作者：Murata Minoru^*

来源：Revista Matematica Iberoamericana, 2011, 27(3): 885-907.

DOI：10.4171/rmi/656

• Heat equation
• rotationally symmetric Riemannian manifold
• nonnegatiye solution
• integral representation
• uniqueness
• semismall perturbation
• Laplace operator
• Martin boundary

Let M be a rotationally symmetric Riemannian manifold. and Delta be the Laplace-Beltrami operator on M. We establish a necessary and sufficient condition for the constant function 1 to be a semismall perturbation of -Delta+1 on M, and give optimal sufficient conditions for uniqueness of nonnegative solutions of the Cauchy problem to the heat equation. As an application, we determine the structure of all nonnegative solutions to the heat equation on M x (0, T).

• 出版日期2011