Journal of Geometric Analysis (J GEOM ANAL )

Publisher: Springer Verlag

Description

The Journal of Geometric Analysis is a forum for the best work in the field of geometric analysis. This journal publishes work which most clearly exhibits the symbiotic relationship among techniques of analysis, geometry, and partial differential equations. The Journal of Geometric Analysis is committed to being the journal of record for important new results that develop the interaction between analysis and geometry. It has established and will maintain the highest standards of innovation and quality in the field. Volume 14 is the 2004 volume. This journal is published four times a year by Mathematica Josephina, Inc., and is printed and distributed by the American Mathematical Society. An author index appears in the last issue of the year. Printed format.

  • Impact factor
    0.86
    Show impact factor history
     
    Impact factor
  • 5-year impact
    0.87
  • Cited half-life
    8.30
  • Immediacy index
    0.17
  • Eigenfactor
    0.00
  • Article influence
    1.05
  • Other titles
    Journal of geometric analysis (Online), Journal of geometric analysis
  • ISSN
    1050-6926
  • OCLC
    62311284
  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

Springer Verlag

  • Pre-print
    • Author can archive a pre-print version
  • Post-print
    • Author can archive a post-print version
  • Conditions
    • Authors own final version only can be archived
    • Publisher's version/PDF cannot be used
    • On author's website or institutional repository
    • On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
    • Published source must be acknowledged
    • Must link to publisher version
    • Set phrase to accompany link to published version (The original publication is available at www.springerlink.com)
    • Articles in some journals can be made Open Access on payment of additional charge
  • Classification
    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: Let M⊂S 4 be a complete orientable hypersurface with constant scalar curvature. For any v∈R 5, let us define the two real functions $l_{v}, f_{v}:M\to{\bf R}$ on M by l v (x)=〈x,v〉 and f v (x)=〈ν(x),v〉 with ν:M→S 4 a Gauss map of M. In this paper, we show that if we have that l v =λf v for some nonzero vector v∈R 5 and some real number λ, then M is either totally umbilical (a Euclidean sphere) or M is a Cartesian product of Euclidean spheres. We will also show with an example that the completeness condition is needed in this theorem.
    Journal of Geometric Analysis 10/2014;
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    ABSTRACT: We introduce a new biholomorphically invariant metric based on Fefferman’s invariant Szegő kernel and investigate the relation of the new metric to the Bergman and Carathéodory metrics. A key tool is a new absolutely invariant function assembled from the Szegő and Bergman kernels.
    Journal of Geometric Analysis 01/2014;
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    ABSTRACT: In this paper, we prove the existence of nontrivial nonnegative solutions to a class of elliptic equations and systems which do not satisfy the Ambrosetti–Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth at ∞. The known results without the AR condition in the literature only involve nonlinear terms of polynomial growth. We will use suitable versions of the Mountain Pass Theorem and Linking Theorem introduced by Cerami (Istit. Lombardo Accad. Sci. Lett. Rend. A, 112(2):332–336, 1978 Ann. Mat. Pura Appl., 124:161–179, 1980). The Moser–Trudinger inequality plays an important role in establishing our results. Our theorems extend the results of de Figueiredo, Miyagaki, and Ruf (Calc. Var. Partial Differ. Equ., 3(2):139–153, 1995) and of de Figueiredo, do Ó, and Ruf (Indiana Univ. Math. J., 53(4):1037–1054, 2004) to the case where the nonlinear term does not satisfy the AR condition. Examples of such nonlinear terms are given in Appendix A. Thus, we have established the existence of nontrivial nonnegative solutions for a wider class of nonlinear terms.
    Journal of Geometric Analysis 01/2014;
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    ABSTRACT: We introduce the Besov space $\dot{B}^{0,L}_{1,1}$ associated with the Schrödinger operator L with a nonnegative potential satisfying a reverse Hölder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space $H_{L}^{1}$ associated with the Schrödinger operator via the Littlewood–Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that $\dot{B}^{0,L}_{1,1}$ is a subspace of $H_{L}^{1}$ .
    Journal of Geometric Analysis 01/2014;
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    ABSTRACT: In this paper, we first establish a constant rank theorem for the second fundamental form of the convex level sets of harmonic functions in space forms. Applying the deformation process, we prove that the level sets of the harmonic functions on convex rings in space forms are strictly convex. Moreover, we give a lower bound for the Gaussian curvature of the convex level sets of harmonic functions in terms of the Gaussian curvature of the boundary and the norm of the gradient on the boundary.
    Journal of Geometric Analysis 01/2014;
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    ABSTRACT: We use a new approach that we call unification to prove that standard weighted double bubbles in n-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight) double bubble theorem (Hass et al., Electron. Res. Announc. Am. Math. Soc., 1(3):98–102, 1995; Hutchings et al., Ann. Math., 155(2):459–489, 2002; Reichardt, J. Geom. Anal., 18(1):172–191, 2008). As part of the proof, we introduce a striking new symmetry argument for showing that a minimizer must be a surface of revolution.
    Journal of Geometric Analysis 01/2014;
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    ABSTRACT: We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.
    Journal of Geometric Analysis 11/2013;
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    ABSTRACT: We define $\lambda(r)$-convergence, which is a generalization of nontangential convergence in the unit disc. We prove Fatou-type theorems on almost everywhere nontangential convergence of Poisson-Stiltjes integrals for general kernels $\{\varphi_r\}$, forming an approximation of identity. We prove that the bound \md0 \limsup_{r\to 1}\lambda(r) \|\varphi_r\|_\infty<\infty \emd is necessary and sufficient for almost everywhere $\lambda(r)$-convergence of the integrals \md0 \int_\ZT \varphi_r(t-x)d\mu(t). \emd
    Journal of Geometric Analysis 10/2013;
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    ABSTRACT: Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces including tori and Klein bottles is extended to a three-parametric family of tori and Klein bottles minimally immersed in spheres. Extremal spectral properties of the metrics on these surfaces are investigated. These metrics include i) both metrics extremal for the first non-trivial eigenvalue on the torus, i.e. the metric on the Clifford torus and the metric on the equilateral torus and ii) the metric maximal for the first non-trivial eigenvalue on the Klein bottle.
    Journal of Geometric Analysis 08/2013;
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    ABSTRACT: We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak isoperimetric inequality.
    Journal of Geometric Analysis 08/2013;