Five Gaps in Mathematics

@article{Bahri2015FiveGI,
  title={Five Gaps in Mathematics},
  author={Abbas Bahri},
  journal={Advanced Nonlinear Studies},
  year={2015},
  volume={15},
  pages={289 - 319}
}
  • A. Bahri
  • Published 2015
  • Mathematics
  • Advanced Nonlinear Studies
Abstract In this article we present a careful survey and critique of 5 landmark results and methods that seem to have played a pivotal role in the development of Mathematics since 1984. This article conveys the slow development of our understanding over the years and could not have been possible without the numerous communications with some authors of these articles as well as conversations with other friends and collaborators. The key contribution and the kindness of these colleagues is hereby… Expand
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References

SHOWING 1-10 OF 41 REFERENCES
Instantons and Four-Manifolds
This volume has been designed to explore the confluence of techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensionalExpand
Width and finite extinction time of Ricci flow
This is an expository article with complete proofs intended for a general non-specialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call the width, of aExpand
DIFFERENTIAL TOPOLOGY
This paper is to propose solutions to selected exercises in Differential Topology by Guillemin and Pollack, [1], and to comment on certain proofs in the book. Although the sections covered in thisExpand
Monopoles and Three-Manifolds
Preface 1. Outlines 2. The Seiberg-Witten equations and compactness 3. Hilbert manifolds and perturbations 4. Moduli spaces and transversality 5. Compactness and gluing 6. Floer homology 7.Expand
Pseudo-orbits of Contact Forms
This is a brief summary of a paper to appear, where I developed some tools in order to study the Weinstein conjecture [1]. This conjecture states that any contact vector-field on a compact contactExpand
Topological Remarks–Critical Points at Infinity and String Theory
Abstract We take the example of the standard geodesics problem on S2 to show how the point to circle Morse relations in the periodic orbits variational problem for contact vector-fields lead directlyExpand
A Course in Minimal Surfaces
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differentialExpand
Multiple Integrals in the Calculus of Variations
Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary valueExpand
Another look at Sobolev spaces
The standard seminorm in the space $W^{s,p}$, with $s$<$1$, does not converge, when $s$ approaches $1$, to the corresponding $W^{1,p}$ seminorm. We prove that continuity is restored provided weExpand
Riemannian Geometry
THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss'sExpand
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