Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds

Chin-Yu Hsiao; George Marinescu; Huan Wang

doi:10.1007/s12220-022-00990-4

Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds

J Geom Anal. 2022;32(11):266. doi: 10.1007/s12220-022-00990-4. Epub 2022 Aug 18.

Authors

Chin-Yu Hsiao¹, George Marinescu^{2

3}, Huan Wang⁴

Affiliations

¹ Institute of Mathematics, Academia Sinica, Taipei, Taiwan.
² Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany.
³ Institute of Mathematics 'Simion Stoilow', Romanian Academy, Bucharest, Romania.
⁴ Tong Jing Nan Lu 798, Suzhou, People's Republic of China.

Abstract

We prove a Bochner-Kodaira-Nakano formula and establish Szegő kernel expansions on complete strictly pseudoconvex CR manifolds with transversal CR $R$ -action under certain natural geometric conditions. As a consequence we show that such manifolds are locally CR embeddable.

Keywords: Bochner–Kodaira–Nakano formula; CR manifolds; Kohn Laplacian; Szegő kernel.