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Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature (2412.08500v1)
Published 11 Dec 2024 in math.DG and math.AP
Abstract: In this paper we study positive solutions to the CR Yamabe equation in noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that the Heisenberg group $\mathbb{H}1$ is the only (complete) Sasakian space with nonnegative Tanaka-Webster scalar curvature admitting a (nontrivial) positive solution. Moreover, under some natural assumptions, we prove this strong rigidity result in higher dimensions, extending the celebrated Jerison-Lee's result to curved manifolds.