Related papers: The Schwarz Lemma: An Odyssey
The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.
A stroll taken around the landscape of Ramsey's Theory. One way first, "Down from infinite to finite", then, another way, "Up from disorder to order". An expose' made at the "Rencontres arithme'tique et combinatoire", Saint-Etienne, june…
The converse of Fortin's Lemma in Banach spaces is established in this Note.
The Schwarz lemmas are well-known characterizations for holomorphic maps and we exhibit two examples of their applications. For a sequence family of biholomorphisms $f_j$, it is useful to determine the location of $f_j(q)$ for a fixed point…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
In this work, we extend the well known Brezis-Lieb Lemma to the Orlicz space.
The purpose of this note is to introduce and study a relativistic motion whose acceleration, in proper time, is given by a white noise. We begin with the flat case of special relativity, continue with the case of general relativity, and…
In this paper, we extend the notion of Schwarz reflection principle for smooth minimal surfaces to the discrete analogues for minimal surfaces, and use it to create global examples of discrete minimal nets with high degree of symmetry.
These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
These are the lecture notes for the introductory course on Whitehead, Reidemeister and Ray-Singer torsions, given by the author at the University of Zurich in Spring semester 2014.
Brief lecture notes for a course about random matrices given at the University of Cambridge.
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…
This paper studies the interpretation of physics near a Schwarzschild black hole. A scenario for creation and growth is proposed that avoids the conundrum of information loss. In this picture the horizon recedes as it is approached and has…
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary…