Journal•ISSN: 1050-6926
Journal of Geometric Analysis
Springer Science+Business Media
About: Journal of Geometric Analysis is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Differential geometry & Holomorphic function. It has an ISSN identifier of 1050-6926. Over the lifetime, 2651 publications have been published receiving 34552 citations.
Topics: Differential geometry, Holomorphic function, Bounded function, Curvature, Boundary (topology)
Papers published on a yearly basis
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TL;DR: There is a nonzero weak solution to the Euler equations of time-dependent incompressible fluid flow in the plane such that this solution has compact support in space-time.
Abstract: There exists a nonzero weak solution to the Euler equations of time-dependent incompressible fluid flow in the plane such that this solution has compact support in space-time.
355 citations
TL;DR: In this article, the authors studied fine properties of quasiplurisubharmonic functions on compact Kahler manifolds and showed that locally pluripolar sets are globally quasi-pluripolar.
Abstract: We study fine properties of quasiplurisubharmonic functions on compact Kahler manifolds. We define and study several intrinsic capacities which characterize pluripolar sets and show that locally pluripolar sets are globally “quasi-pluripolar.”
320 citations
TL;DR: In this paper, the authors characterize such measures as the ones that obey Jensen's inequality for all quasiconvex functions with the appropriate growth at infinity and show that any measure determined by convergence is in fact generated by a sequence convergent in a stronger sense.
Abstract: Oscillatory properties of a weak convergent sequence of functions bounded inL
p
, 1 ≤p ≤ ∞, may be summarized by the parametrized measure it generates. When such a measure is generated by the gradients of a sequence of functions bounded inH
1,p
, it must have special properties. The purpose of this paper is to characterize such parametrized measures as the ones that obey Jensen’s inequality for all quasiconvex functions with the appropriate growth at infinity. We have found subtle differences between the casesp < ∞ andp = ∞. A consequence is that any measure determined by biting convergence is in fact generated by a sequence convergent in a stronger sense. We also give a few applications.
237 citations
TL;DR: In this article, the fine properties of the mean curvature PDE were investigated, and the Hausdorff measure of level sets and smoothness was obtained for graphs with level sets.
Abstract: We continue our investigation [6,7] (see also [4], etc.) of the generalized motion of sets via mean curvature by the level set method. We study more carefully the fine properties of the mean curvature PDE, to obtain Hausdorff measure estimates of level sets and smoothness whenever the level sets are graphs.
221 citations
TL;DR: In this paper, the authors studied codimension 1 rectifiable sets in Carnot groups and extended classical De Giorgi's rectifiability and divergence theorems to the setting of step 2 groups.
Abstract: In this article we study codimension 1 rectifiable sets in Carnot groups and we extend classical De Giorgi ’s rectifiability and divergence theorems to the setting of step 2 groups Related problems in higher step Carnot groups are discussed, pointing on new phenomena related to the blow up procedure
210 citations