Rigidity result for semilinear subelliptic partial differential equation on Cauchy-Riemannian manifolds

Prof. Xinan Ma (University of Science and Technology of China, Hefei)
Rigidity result for semilinear subelliptic partial differential equation on Cauchy-Riemannian manifolds

Abstract
On CR manifolds we get the rigidity result, i.e., subelliptic equations have no other solution than some constant at least when parameters are in a certain range, thus solved also the conjecture of Xiaodong Wang in his Math. Z. 2022 paper, in Riemannian geometry version the corresponding result was got by Bidaut Veron- Veron in 1991.The rigidity result also deduces the best constant for the  Folland-Stein Sobolev inequality on closed CR manifolds, when the CR manifold is S²ⁿ⁺¹ this inequality was obtained by Frank-Lieb in 2012 . This is a joint work with Qianzhong Ou and Tian Wu.