4维ricci -平坦ALE空间的重整化体积

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2023-03-01 DOI:10.4310/jdg/1683307004

Olivier Biquard, Hans-Joachim Hein

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引用次数: 0

摘要

我们引入了$4$维ricci -平坦ALE空间重归一化体积的自然定义。然后证明重整体积总是小于或等于零，当且仅当ALE空间与其渐近锥等距时，体积等于零。目前唯一已知的4维ricci平面ALE空间的例子是Kronheimer的引力瞬子和它们的商，它们也被认为是唯一可能的特殊完整的例子。我们根据Kronheimer的周期图计算这些空间的重归一化体积。

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The renormalized volume of a $4$-dimensional Ricci-flat ALE space

We introduce a natural definition of the renormalized volume of a $4$-dimensional Ricci-flat ALE space. We then prove that the renormalized volume is always less or equal than zero, with equality if and only if the ALE space is isometric to its asymptotic cone. Currently the only known examples of $4$-dimensional Ricci-flat ALE spaces are Kronheimer’s gravitational instantons and their quotients, which are also known to be the only possible examples of special holonomy. We calculate the renormalized volume of these spaces in terms of Kronheimer’s period map.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.