Abstract
In this paper, the authors establish a generalized maximum principle for pseudo-Hermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced. Moreover, they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles. Finally, they give some applications of these generalized maximum principles.
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This work was supported by the National Natural Science Foundation of China (Nos. 11771087, 12171091), LMNS, Fudan, Jiangsu Funding Program for Excellent Postdoctoral Talent (No. 2022ZB281) and the Fundamental Research Funds for the Central Universities (No. 30922010410).
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Dong, Y., Yu, W. Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds. Chin. Ann. Math. Ser. B 43, 949–976 (2022). https://doi.org/10.1007/s11401-022-0372-z
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DOI: https://doi.org/10.1007/s11401-022-0372-z