3 citations · 6 across the 4 of their papers we have counts for
16 papers
Quasi-states and symplectic intersections
Michael Entov, Leonid Polterovich
We establish a link between symplectic topology and a recently emerged branch of functional analysis called the theory of quasi-states and quasi-measures. In the symplectic context…
Sign and area in nodal geometry of Laplace eigenfunctions
Fedor Nazarov, Leonid Polterovich, Mikhail Sodin
The paper deals with asymptotic nodal geometry for the Laplace-Beltrami operator on closed surfaces. Given an eigenfunction f corresponding to a large eigenvalue, we study local as…
Calabi quasimorphisms for the symplectic ball
Paul Biran, Michael Entov, Leonid Polterovich
We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms.…
Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
Gabriel P. Paternain, Leonid Polterovich, Karl Friedrich Siburg
We consider Lagrangian submanifolds lying on a fiberwise strictly convex hypersurface in some cotangent bundle or, respectively, in the domain bounded by such a hypersurface. We es…
Calabi quasimorphism and quantum homology
Michael Entov, Leonid Polterovich
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value…
A growth gap for diffeomorphisms of the interval
Leonid Polterovich, Mikhail Sodin
Given an orientation-preserving diffeomorphism of the interval [0;1], consider the uniform norm of the differential of its n-th iteration. We get a function of n called the growth…