黎曼流形的抛物性与度量的共形形变

Parabolicity and Conformal Deformations of the Metrics on a Riemannian Manifold

借助于黎曼流形的抛物性概念研究黎曼度量的共形形变问题, 证明了Gauss曲率小于某负常数的非紧完备2维黎曼流形其度量不可能共形形变到具有非负Gauss曲率的完备度量.

Conformal deformations of the Metrics on a Riemannian manifold are investigated by using parabolicity, and it is proved that if a complete noncompact 2-dimensional Riemannian manifold has Gauss curvature less than a negative constant, its metric can not be conformally deformed to a complete metric with nonnegative Gauss curvature.