THE SHARP ENERGY-CAPACITY INEQUALITY

DOI10.1142/S0219199710003889zbMath1200.53077arXiv0808.1592MaRDI QIDQ3577793

Michael Usher

Publication date: 23 July 2010

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1592

zbMATH Keywords

Hofer-Zehnder capacityspectral invariantsdisplacement energy

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Symplectic aspects of Floer homology and cohomology (53D40)

Related Items (24)

Hamiltonian pseudo-rotations of projective spaces ⋮ Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories ⋮ Some quantitative results in \(\mathcal {C}^0\) symplectic geometry ⋮ On the Hofer-Zehnder conjecture ⋮ Viterbo conjecture for Zoll symmetric spaces ⋮ The symplectic cohomology of magnetic cotangent bundles ⋮ Floer theory and reduced cohomology on open manifolds ⋮ Proof of the simplicity conjecture ⋮ Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms ⋮ Coisotropic displacement and small subsets of a symplectic manifold ⋮ The sharp energy-capacity inequality on convex symplectic manifolds ⋮ Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product ⋮ Spectral killers and Poisson bracket invariants ⋮ Disjoint superheavy subsets and fragmentation norms ⋮ DESCENT AND C⁰-RIGIDITY OF SPECTRAL INVARIANTS ON MONOTONE SYMPLECTIC MANIFOLDS ⋮ Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds ⋮ The action spectrum and \(C^0\) symplectic topology ⋮ Symplectic structure perturbations and continuity of symplectic invariants ⋮ Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms ⋮ Barcodes and area-preserving homeomorphisms ⋮ Spectral invariants of distance functions ⋮ A brief survey of the spectral numbers in floer homology ⋮ Bounds on spectral norms and barcodes ⋮ Coisotropic rigidity and \(C^0\)-symplectic geometry

Cites Work

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• Hamiltonian dynamics on convex symplectic manifolds
• Pseudo holomorphic curves in symplectic manifolds
• Arnold conjecture and Gromov-Witten invariant
• Tight contact structures and Seiberg-Witten invariants
• On the action spectrum for closed symplectically aspherical manifolds
• Hofer-Zehnder capacity and length minimizing Hamiltonian paths
• The geometry of symplectic energy
• On symplectic fillings
• A few remarks about symplectic filling
• Gromov-Witten invariants and pseudo symplectic capacities
• On the topological properties of symplectic maps
• Spectral numbers in Floer theories
• FLOER MINI-MAX THEORY, THE CERF DIAGRAM, AND THE SPECTRAL INVARIANTS
• Symplectic embeddings of polydisks

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