Related papers: Notes on a paper of Mess
Notes for a one semester course. The notes contain a description of compact three dimensional Seifert fibered spaces and a classification up to homeomorphism of compact three dimensional Seifert fibered spaces with non-empty boundary.
Recently, an axially symmetric spacetime with causality violation is appeared in Ref. [1]. There, author presented a type III metric with vanishing expansion, shear and twist. The matter-energy represents a pure radial field with a negative…
We define a discrete Menger-type curvature of d+2 points in a real separable Hilbert space H by an appropriate scaling of the squared volume of the corresponding (d+1)-simplex. We then form a continuous curvature of an Ahlfors d-regular…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…
The 1983 book, free at last, with corrections and bookmarks. From the original troff, but now with CM (TeX) fonts.
A detailed re-examination of the seminal paper on special relativity, taking into account recent work on the physical interpretation of the space-time Lorentz transformation as well as the modern understanding of classical elecromagnetism…
This paper is mostly a collection of ideas already published by various authors, some of them even a long time ago. Its intention is to bring the reader to know some rather unknown papers of different fields that merit interest and to show…
This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I…
We correct an inaccuracy in a previous article [Auscher, Pascal; Bernicot, Fr\'ed\'eric; Zhao, Jiman. Maximal regularity and Hardy spaces. Collect. Math. 59 (2008), no. 1, 103-127.]
Classical geometry of de Sitter spacetime is reviewed in arbitrary dimensions. Topics include coordinate systems, geodesic motions, and Penrose diagrams with detailed calculations.
It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After reviewing subsequent progress that has been made on this topic,…
Rejoinder to the discussion by Hino (2025) and Pardo-Fern\'andez (2025) of Chac\'on and Fern\'andez Serrano (2025), a special paper (with discussion) published in Annals of the Institute of Statistical Mathematics.
In this note, we use isothermic coordinate systems to explore global properties of space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.
These are notes of a talk I gave in a seminar at the University of Pennsylvania summarizing results in the Ph.D. thesis of Michael Mueter obtained under the direction of Wolfgang Meyer at the University of Muenster. His thesis on…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
Lecture notes on Finsler Geometry
More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric would be of order one at the Planck scale, leading to large fluctuations in spacetime geometry and topology, which he termed "spacetime foam." In this…
This article was originally published in Topology 31 (1992). The present hyperTeXed redaction corrects a few typographical errors and updates the references.
Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and…