Szego kernel asymptotics and Morse inequalities on CR manifolds
Artikel i vetenskaplig tidskrift, 2012

Let X be an abstract compact orientable CR manifold of dimension 2n-1, n >= 2, and let L-k be the k-th tensor power of a CR complex line bundle L over X. We assume that condition Y (q) holds at each point of X. In this paper we obtain a scaling upper-bound for the Szego kernel on (0, q)-forms with values in L-k, for large k. After integration, this gives weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities. We apply the strong Morse inequalities to the embedding of some convex-concave manifolds.



Chin-Yu Hsiao

Göteborgs universitet

Chalmers, Matematiska vetenskaper

G. Marinescu

Institute of Mathematics of the Romanian Academy

Universitat zu Koln

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 271 509-553