Geometrically and topologically random surfaces in a closed hyperbolic 3-manifold

IF 1.6 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2026-03-17 DOI:10.1112/topo.70068

Jeremy Kahn, Vladimir Marković, Ilia Smilga

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引用次数: 0

Abstract

We study the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold $M$ . In particular, we describe $PSL (2, R)$ invariant measures on the Grassmann bundle $G_{2} (M)$ which arise as limits of random minimal surfaces. We show that if $M$ contains at least one totally geodesic subsurface then every topological limiting measure is totally scarring (i.e., supported on the totally geodesic locus), while we prove that geometrical limiting measures are never totally scarring.

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闭双曲3流形的几何和拓扑随机曲面

研究了闭双曲3流形M ${\bf {M}}$中几何和拓扑近测地线随机曲面的分布。特别地，我们描述PSL (2)，R)$ {\bf {PSL}}(2,\mathbb {R})$在Grassmann束g2 (M)$ {\mathcal {G}}_2({\bf {M}})$上作为随机极小曲面极限出现的不变测度。我们证明了如果M ${\bf {M}}$包含至少一个完全测地线子曲面，则每个拓扑极限测度都是完全疤痕的（即，支持在完全测地线轨迹上），而我们证明了几何极限测度从不是完全疤痕的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.