On the adjoint action of the group of symplectic diffeomorphisms

2020/09/14 by László Lempert, Lempert, Laszlo
Mathematics · #53D05 #58D19 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2009.06729

openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the action of Hamiltonian diffeomorphisms of a compact symplectic manifold (X,ω) on C^∞(X) and on functions C^∞(X)→ \mathbb R. We describe various properties of invariant convex functions on C^∞(X). Among other things we show that continuous convex functions C^∞(X)→ \mathbb R that are invariant under the action are automatically invariant under so called strict rearrangements and they are continuous in the sup norm topology of C^∞(X); but this is not generally true if the convexity condition is dropped.

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