Journal•ISSN: 0022-040X
Journal of Differential Geometry
Lehigh University
About: Journal of Differential Geometry is an academic journal published by Lehigh University. The journal publishes majorly in the area(s): Scalar curvature & Curvature. It has an ISSN identifier of 0022-040X. Over the lifetime, 2367 publications have been published receiving 175533 citations. The journal is also known as: J. Differential Geometry & J. Differ. Geom..
Papers published on a yearly basis
Papers
More filters
3,014 citations
TL;DR: In this paper, it was shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian, and some of the implications of modern ideas in mathematics for super-ymmetric theories are discussed.
Abstract: It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.
1,625 citations
TL;DR: In this article, a homotopy theoretic criterion for imbedding (relatively) a topological 2-handle in a smooth four-dimensional manifold with boundary was proposed.
Abstract: 0. Introduction Manifold topology enjoyed a golden age in the late 1950's and 1960's. Of the mysteries still remaining after that period of great success the most compelling seemed to lie in dimensions three and four. Although experience suggested that manifold theory at these dimensions has a distinct character, the dream remained since my graduate school days that some key principle from the high dimensional theory would extend, at least to dimension four, and bring with it the beautiful adherence of topology to algebra familiar in dimensions greater than or equal to five. There is such a principle. It is a homotopy theoretic criterion for imbedding (relatively) a topological 2-handle in a smooth four-dimensional manifold with boundary. The main impact, as outlined in §1, is to the classification of 1-connected 4-manifolds and topological end recognition. However, certain applications to nonsimply connected problems such as knot concordance are also obtained. The discovery of this principle was made in three stages. From 1973 to 1975 Andrew Casson developed his theory of "flexible handles". These are certain pairs having the proper homotopy type of the common place open 2-handle H = (D X D, dD X D) but "flexible" in the sense that finding imbeddings is rather easy; in fact imbedding is implied by a homotopy theoretic criterion. It was clear to Casson that: (1) no known invariant—link theoretic
1,566 citations
TL;DR: In this paper, a weak solution of the nonlinear PDE is proposed, which asserts each level set evolves in time according to its mean curvature, existing for all time.
Abstract: We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set ⌈0 a unique generalized motion by mean curvature, existing for all time. We investigate the various geometric properties and pathologies of this evolution.
1,415 citations
TL;DR: In this paper, the authors consider a compact, uniformly convex w-dimensional surface M = Mo without boundary, which is smoothly imbedded in R. They show that the behavior of grain boundaries in annealing pure metal can be modeled by a diffeomorphism.
Abstract: The motion of surfaces by their mean curvature has been studied by Brakke [1] from the viewpoint of geometric measure theory. Other authors investigated the corresponding nonparametric problem [2], [5], [9]. A reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal. In this paper we take a more classical point of view: Consider a compact, uniformly convex w-dimensional surface M = Mo without boundary, which is smoothly imbedded in R. Let Mo be represented locally by a diffeomorphism
1,331 citations