| Abstract: |
| One of the most important characterizations of the conservation property of the heat of a Riemannian manifold is a Liouville type property of the solution of the heat equation. This is called the Khasminskii test. A heat equation with killing inside is never conservative; however, it may enjoy the Liouville type property. Namely, the characterization fails. In this talk, we will propose a generalized conservation property and show that it is characterized by the Khasminskii test. |
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