Related papers: Weil-Petersson Metric Geometry Quick Overview
We construct Weil-Petersson (WP) geodesic rays with minimal filling non-uniquely ergodic ending lamination which are recurrent to a compact subset of the moduli space of Riemann surfaces. This construction shows that an analogue of the…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
In this paper, a new structure is defined on a topological space that equips the space with a concept of distance in order to do that firstly, a generalization of quasi-pseudo-metric space named R.O-metric space is introduced, and some of…
We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applying equally to Rips filtrations and Cech filtrations for any…
Application of the noncommutative geometry to several physical models is considered.
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.
This is a review of the fundamental concepts of general topology.
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
We build on recent work linking backward and forward W2-projections in convex order with the recently introduced metric extrapolation problem to derive new quantitative stability estimates for both problems.
In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
In this survey article we gather classical as well as recent results on minimal geodesics of Riemannian or Finsler metrics, giving special attention to the two-dimensional case. Moreover, we present open problems together with some first…
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…