19. Juli 2023, 10:30 in VSP1, 3.31
Chaofeng Zhu (Nankai University)
Global Mountain Pass Points and Applications to Minimal Period Problems in Hamiltonian Systems
In this talk, we introduce the notion of the global mountain pass points. Then we show that under certain conditions, there exists either a non-trivial minimal point or a global mountain pass point. As an application, we show that for each $\tau>0$, a strictly convex super-linear autonomous Hamiltonian system with brake symmetry has a periodic orbit with minimal period $\tau$.
Bernhelm Booss-Bavnbek (Roskilde University)
The Calderón Projection for Elliptic Differential Operators on Manifolds with Boundary: Concept, Meaning, and Deformation Properties
A key result in spectral geometry is the calculation of the spectral flow of a curve of elliptic boundary value problems over a smooth compact manifold with boundary (belonging to the realm of functional analysis) by the Maslov index of related curves of Lagrangian subspaces over the boundary (belonging to the realm of symplectic geometry). I shall explain obstructions of a general validity of this Spectral Flow Theorem and how to overcome these obstructions by natural assumptions regarding the inner weak unique continuation property (UCP) that imply the continuity of families of Calderón projections. I shall give details of a simple proof of that crucial continuity. This is joint work with Chaofeng Zhu.