相关论文: Weil-Petersson Metric Geometry Quick Overview
We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on and the understanding of infinite dimensional Teichm\"{u}ller spaces the reader is directed…
A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and…
We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm\"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of…
We introduce a method for constructing Weil-Petersson (WP) geodesics with certain behavior in the Teichm\"{u}ller space. This allows us to study the itinerary of geodesics among the strata of the WP completion and its relation to subsurface…
We study the Weil-Petersson geometry for holomorphic families of Riemann Surfaces equipped with the unique conical metric of constant curvature -1.
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length…
Some examples and basic properties of ultrametric spaces are briefly discussed.
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The…
We consider the Riemann moduli space $\mathcal M_{\gamma}$ of conformal structures on a compact surface of genus $\gamma>1$ together with its Weil-Petersson metric $g_{\mathrm{WP}}$. Our main result is that $g_{\mathrm{WP}}$ admits a…
This is a survey paper on the topic of Weil-Petersson geometry of Teichmuller spaces. Even though historically the subject has been developed as a branch of complex analysis, the treatment here is from the view-point of differential…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
We study Weil-Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of…
These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…
A 2008 general overview on Weil-Petersson geometry is offered. A preliminary plan for the subsequent CBMS lectures at Central Connecticut State University is included. Mirzakhani's solution of Witten-Kontsevich is not included - this work…
We consider the Weil--Petersson (WP) metric on the modular surface. We lift WP geodesics to the universal cover of the modular surface and analyse geometric properties of the lifts as paths in the hyperbolic metric on the universal cover.…