Abstract.
We extend our earlier work in [TiZ1], where an analytic approach to the Guillemin-Sternberg geometric quantization conjecture [GuSt] was developed, to the case of manifolds with boundary. We also give a general quantization formula that works for both regular and singular reductions. As simple applications, we prove an analytic analogue of the relative residue formula of Guillemin-Kalkman [GuK] and Martin [M], as well as a Guillemin-Sternberg type formula for singular reductions under circle actions.
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Submitted: February 1997, revised: January 1998 and July 1998, final version: March 1999.
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Tian, Y., Zhang, W. Quantization Formula for Symplectic Manifolds with Boundary. GAFA, Geom. funct. anal. 9, 596–640 (1999). https://doi.org/10.1007/s000390050097
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DOI: https://doi.org/10.1007/s000390050097