2022/12/04 by Lev Buhovsky, Shira Tanny, Buhovsky, Lev +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2212.01872
openalex publication_date 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a local-to-global inequality for spectral invariants of Hamiltonians whose supports have a ``large enough" tubular neighborhood on semipositive symplectic manifolds. In particular, we present the first examples of such an inequality when the Hamiltonians are not necessarily supported in domains with contact type boundaries, or when the ambient manifold is irrational. This extends a series of previous works studying locality phenomena of spectral invariants. A main new tool is a lower bound, in the spirit of Sikorav, for the energy of Floer trajectories that cross the tubular neighborhood against the direction of the negative-gradient vector field.