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Szego kernel asymptotics and Morse inequalities on CR manifolds

Chin-Yu Hsiao (Institutionen för matematiska vetenskaper) ; G. Marinescu
Mathematische Zeitschrift (0025-5874). Vol. 271 (2012), 1-2, p. 509-553.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: boundary



Denna post skapades 2012-08-09. Senast ändrad 2012-08-13.
CPL Pubid: 161335

 

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Matematik

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