Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds

Date

2020-10-01

Author

Şirikçi, Nil İpek

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

382
views

0
downloads

We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function, a result on this orbit's Conley-Zehnder index and another result on the Morse indices for constant sectional curvature manifolds the utilization of which to prove nondisplaceability is new.

Subject Keywords

Applied Mathematics, Mathematics (miscellaneous)

URI

https://hdl.handle.net/11511/57974

Journal

RESULTS IN MATHEMATICS

DOI

https://doi.org/10.1007/s00025-020-01279-0

Collections

Department of Economics, Article

Suggestions

OpenMETU
Core

Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01) Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
Legendrian realization in convex Lefschetz fibrations and convex stabilizations Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01) We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
Error estimates for space-time discontinuous Galerkin formulation based on proper orthogonal decomposition Akman, Tuğba (Informa UK Limited, 2017-01-01) In this study, proper orthogonal decomposition (POD) method is applied to diffusion-convection-reaction equation, which is discretized using spacetime discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and spacetime projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence ra...
Piecewise polynomials with different smoothness degrees on polyhedral complexes ALTINOK BHUPAL, SELMA; Sipahi, Neslihan Os (Informa UK Limited, 2019-05-01) For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the techni...

Citation Formats

N. İ. Şirikçi, “Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds,” RESULTS IN MATHEMATICS, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57974.