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Biharmonic Caloric Functions On Open Manifolds
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For a complete open Riemannian manifold with nonnegative Ricci curvature, we show that the dimension of the space of ancient biharmonic caloric functions with polynomial growth is bounded by the degree of growth times the dimension of biharmonic functions with the same growth. Moreover, we investigate biharmonic caloric functions on Euclidean spaces.
Title: Biharmonic Caloric Functions On Open Manifolds
Description:
For a complete open Riemannian manifold with nonnegative Ricci curvature, we show that the dimension of the space of ancient biharmonic caloric functions with polynomial growth is bounded by the degree of growth times the dimension of biharmonic functions with the same growth.
Moreover, we investigate biharmonic caloric functions on Euclidean spaces.
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