作者:Xianzhe Dai , Guofang Wei , Zhenlei Zhang
来源:[J].Advances in Mathematics(IF 1.373), 2018, Vol.325, pp.1-33Elsevier
摘要:Abstract(#br)We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the L 2 Hessian estimate to manifolds with integral Ricci l...
作者:Xianzhe Dai , Weiping Zhang
来源:[J].Advances in Mathematics(IF 1.373), 2015, Vol.279, pp.291-306Elsevier
摘要:Abstract(#br)In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah–Patodi–Singer, which is for odd dimensional manifolds. It is associated to K 1 representatives on even dimensional manifolds and ...
作者:Xianzhe Dai , Kefeng Liu , Xiaonan Ma
来源:[J].Comptes rendus - Mathématique(IF 0.477), 2004, Vol.339 (3), pp.193-198Elsevier
摘要:Abstract(#br)We study the asymptotics of the Bergman kernel and the heat kernel of the spin c Dirac operator on high tensor powers of a line bundle. To cite this article: X. Dai et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).
作者:Xianzhe Dai , Weiping Zhang
来源:[J].Journal of Functional Analysis(IF 1.252), 2006, Vol.238 (1), pp.1-26Elsevier
摘要:Abstract(#br)We establish an index theorem for Toeplitz operators on odd-dimensional spin manifolds with boundary. It may be thought of as an odd-dimensional analogue of the Atiyah–Patodi–Singer index theorem for Dirac operators on manifolds with boundary. In particular, the...
作者:Xianzhe Dai , Weiping Zhang
来源:[J].Journal of Functional Analysis(IF 1.252), 1998, Vol.157 (2), pp.432-469Elsevier
摘要:Abstract(#br)For a continuous curve of families of Dirac type operators we define a higher spectral flow as a K -group element. We show that this higher spectral flow can be computed analytically by η -forms and is related to the family index in the same way as the spectral ...


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