Szego kernel asymptotics and Morse inequalities on CR manifolds

作者：Hsiao Chin Yu^*; Marinescu George

来源：Mathematische Zeitschrift, 2012, 271(1-2): 509-553.

DOI：10.1007/s00209-011-0875-x

Let X be an abstract compact orientable CR manifold of dimension 2n-1, n %26gt;= 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.

• 出版日期2012-6