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Geodesic balls and Chern numbers of Kähler manifolds. (English) Zbl 0788.53065
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 127-135 (1992).
The author gives a summary of his results about the volume of geodesic balls which appeared in [Nagoya Math. J. 116, 181-189 (1989; Zbl 0683.53061)] and which are closely related to the volume conjectures of A. Gray and the reviewer [Acta Math. 142, 157-198 (1979; Zbl 0428.53017)]. He focuses on Kähler manifolds $$M$$ and considers the conjectures in relation with conditions on the generalized Chern numbers or Chern classes, in particular when $$\dim M = 4$$.
For the entire collection see [Zbl 0764.00002].
##### MSC:
 53C55 Global differential geometry of Hermitian and Kählerian manifolds
##### Keywords:
volume of geodesic balls; Kähler manifolds; Chern numbers