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Holomorphic family of strongly pseudoconvex domains in a K\"ahler manifold

math.CV · 2019-08-16 · conditional · novelty 6.0

For any holomorphic family of bounded strongly pseudoconvex domains in a Kähler manifold, the variation of complete Kähler-Einstein metrics is positive definite on the total space when the total domain is strongly pseudoconvex, and extends as a positive current under a scalar-curvature bound.

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  • Holomorphic family of strongly pseudoconvex domains in a K\"ahler manifold math.CV · 2019-08-16 · conditional · none · ref 8

    For any holomorphic family of bounded strongly pseudoconvex domains in a Kähler manifold, the variation of complete Kähler-Einstein metrics is positive definite on the total space when the total domain is strongly pseudoconvex, and extends as a positive current under a scalar-curvature bound.