March 25, 2007
Similar papers 2
June 13, 2009
This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.
November 29, 2005
In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.
September 17, 2022
Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.
May 27, 2008
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
October 11, 2024
This is an English translation of Ludwig Bieberbach's paper ``Remarks on Hilbert's Thirteenth Problem" originally written in German and originally published in Journal f\"ur die Reine und Angewandte Mathematik - 165 (89-92) 1931, along with an addendum to the paper published in 1933. Beiberbach studies under what conditions are there functions of three variables which can or cannot be obtained by combining or nesting functions of two variables. In the addendum, Bieberbach ack...
December 31, 2004
This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an annotated bibliography.
July 13, 2005
This, and its sequel, concern some variations of a classical theorem of A.D. Alexandrov and teh Hopf Lemma.
December 11, 2015
This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.
December 11, 2013
Hilbert's fourth problem asks for the construction and the study of metrics on subsets of projective space for which the projective line segments are geodesics. Several solutions of the problem were given so far, depending on more precise interpretations of this problem, with various additional conditions satisfied. The most interesting solutions are probably those inspired from an integral formula that was first introduced in this theory by Herbert Busemann. Besides that, Bu...
August 16, 2007
The 2007 Midwest Geometry Conference included a panel discussion devoted to open problems and the general direction of future research in fields related to the main themes of the conference. This paper summarizes the comments made during the panel discussion.