THE SHARP ENERGY-CAPACITY INEQUALITY
By Michael Usher. 2008
55 citations recorded by the source corpus.
Using the Oh–Schwarz spectral invariants and some arguments of Frauenfelder, Ginzburg and Schlenk, we show that the π1-sensitive Hofer–Zehnder capacity of any subset of a closed symplectic manifold is less than or equal to its displacement energy. This estimate is sharp, and implies some new extensions of the Non-Squeezing Theorem.
Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e32db3698f48be6df362454c67c993bb75152395
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In Applied Mathematics
In Geometry and Topology
- Sobhan Seyfaddini
- Vincent Humilière
- R. Leclercq
- Michael Usher
- E. Shelukhin
- A. Kislev
- L. Polterovich
- Jun Zhang
In Statistical and Nonlinear Physics
Citations in the corpus
- Coisotropic rigidity and $C^{0}$-symplectic geometry (2013, methodology): “The method of proof is now classical and goes back to Viterbo [24] (see also Usher’s proof of the analogous result [23] for compact manifolds, itself heavily influenced by Frauenfelder–Ginzburg–Schlenk [6]).”
- Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms (2010, background): “3 about the deformed spectral invariants, which is new even in the undeformed case D 0 (though an important special case appears in Usher [62]).”