Rabinowitz

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 43404 Experts worldwide ranked by ideXlab platform

Filipe Dantastorres - One of the best experts on this subject based on the ideXlab platform.

Ali Maalaoui - One of the best experts on this subject based on the ideXlab platform.

Claudianor O Alves - One of the best experts on this subject based on the ideXlab platform.

Sergio H M Soares - One of the best experts on this subject based on the ideXlab platform.

Jungsoo Kang - One of the best experts on this subject based on the ideXlab platform.

  • vanishing of Rabinowitz floer homology on negative line bundles
    Mathematische Zeitschrift, 2017
    Co-Authors: Peter Albers, Jungsoo Kang
    Abstract:

    Following Frauenfelder (Rabinowitz action functional on very negative line bundles, Habilitationsschrift, Munich/Munchen, 2008), Albers and Frauenfelder (Bubbles and onis, 2014. arXiv:1412.4360) we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. Ritter (Adv Math 262:1035–1106, 2014) showed that symplectic homology of these spaces does not vanish, in general. Thus, the theorem \(\mathrm {SH}=0\Leftrightarrow \mathrm {RFH}=0\) (Ritter in J Topol 6(2):391–489, 2013), does not extend beyond the symplectically aspherical situation. We give a conjectural explanation in terms of the Cieliebak–Frauenfelder–Oancea long exact sequence Cieliebak et al. (Ann Sci Ec Norm Super (4) 43(6):957–1015, 2010).

  • Vanishing of Rabinowitz Floer homology on negative line bundles
    Mathematische Zeitschrift, 2016
    Co-Authors: Peter Albers, Jungsoo Kang
    Abstract:

    Following [Fra08, AF14] we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. In [Rit14] Ritter showed that symplectic homology of these spaces does not vanish, in general. Thus, the theorem $\mathrm{SH}=0\Leftrightarrow\mathrm{RFH}=0$, [Rit13], does not extend beyond the symplectically aspherical situation. We give a conjectural explanation in terms of the Cieliebak-Frauenfelder-Oancea long exact sequence [CFO10].Comment: 24 page

  • kunneth formula in Rabinowitz floer homology
    Calculus of Variations and Partial Differential Equations, 2013
    Co-Authors: Jungsoo Kang
    Abstract:

    Rabinowitz Floer homology has been investigated on submanifolds of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study Rabinowitz Floer homology for product manifolds which are not necessarily of contact type. We show for a class of product manifolds that there are infinitely many leafwise intersection points by proving the Kunneth formula for Rabinowitz Floer homology.

  • survival of infinitely many critical points for the Rabinowitz action functional
    Journal of Modern Dynamics, 2011
    Co-Authors: Jungsoo Kang
    Abstract:

    In this paper, we show that if Rabinowitz Floer homology has infinite dimension, there exist infinitely many critical points of a Rabinowitz action functional even though it could be non-Morse. This result is proved by examining filtered Rabinowitz Floer homology.

  • survival of infinitely many critical points for the Rabinowitz action functional
    arXiv: Symplectic Geometry, 2010
    Co-Authors: Jungsoo Kang
    Abstract:

    In this paper, we show that if the Rabinowitz Floer homology has infinite dimension, there exist infinitely many critical points of a Rabinowitz action functional even though it could be non-Morse. This result is proved by examining the filtered Rabinowitz Floer homology.