Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds

Abstract

We obtain estimates showing that on monotone symplectic manifolds (asymptotic) spectral invariants of Hamiltonians which vanish on a non-empty open set, U, descend to Ham_c(M\setminus U) from its universal cover. Furthermore, we show these invariants and are continuous with respect to the C^0-topology on Ham_c(M\setminus U). We apply these results to Hofer geometry and establish unboundedness of the Hofer diameter of $Ha{m}_c(M\setminus U)$ for stably displaceable $U$. We also answer a question of F. Le Roux about $C^0$-continuity properties of the Hofer metric.

17 pages

References in corpus (2)

• Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds
• Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds

Cited by in corpus (10)

• The action spectrum and C^0 symplectic topology
• Quasi-morphisms and quasi-states in symplectic topology
• New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians
• A Hölder-type inequality for the $C^0$ distance and Anosov-Katok pseudo-rotations
• Unboundedness of the Lagrangian Hofer distance in the Euclidean ball
• Heavy subsets and non-contractible trajectories
• Superheavy Lagrangian immersion in 2-torus
• Compactly supported Hamiltonian loops with non zero Calabi invariant
• Stochastic homogenization for variational solutions of Hamilton-Jacobi equations
• Fragmented Hofer's geometry