Journal of Geometric Analysis (J GEOM ANAL )

Publisher: Springer Verlag


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.

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  • Other titles
    Journal of geometric analysis (Online), Journal of geometric analysis
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  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

Springer Verlag

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    • Author can archive a pre-print version
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    • Author can archive a post-print version
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    • Authors own final version only can be archived
    • Publisher's version/PDF cannot be used
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    • On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
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    • Must link to publisher version
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    • Articles in some journals can be made Open Access on payment of additional charge
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Publications in this journal

  • [Show abstract] [Hide abstract]
    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: Wavelet sets that are finite unions of convex sets are constructed in $\mathbb{R}^{n}$ , n≥2, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt{n}$ . In particular, we produce simple wavelet sets in every dimension for dilation by any real scalar greater than 1.
    Journal of Geometric Analysis 04/2013;
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    ABSTRACT: We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-\'Emery Ricci tensor on $M$ is bounded below, then we can obtain an upper bound estimate for the heat kernel of the drifting Laplacian from the upper bound estimates of the heat kernels of the Laplacians on a family of related warped product spaces. We apply these results to study the essential spectrum of the drifting Laplacian on $M$.
    Journal of Geometric Analysis 04/2013;
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    ABSTRACT: Let E be a subset in (n+1)-dimensional Euclidean space with parabolic homogeneity, codimension 1, and with an appropriate surface measure σ associated with it. For certain kinds of parabolic Calderón–Zygmund operators T we prove that the L 2(E,dσ)-boundedness of T is equivalent to the parabolic uniform rectifiability of E. This is a parabolic version of a well-known result of G. David and S. Semmes.
    Journal of Geometric Analysis 01/2013; 23(3).
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    ABSTRACT: For representations in the Cohen class, specific Cohen kernels depending only on one half of the variables are showed to produce two types of representations which can in a natural way be associated with time and frequency windows. This leads to the definition of representations with no interference for signals whose time-frequency content is confined in specific zones. We prove the main properties of these representations in the context of the Cohen class. We study then uncertainty principles at first in connection with support compactness and then in the framework of a general concept of duality among representations.
    Journal of Geometric Analysis 01/2013;

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