Morrey-Campanato spaces on manifolds
Morse-Bott functions with two critical values on a surface
We study Morse-Bott functions with two critical values (equivalently, nonconstant without saddles) on closed surfaces. We show that only four surfaces admit such functions (though in higher dimensions, we construct many such manifolds, e.g. as fiber bundles over already constructed manifolds with the same property). We study properties of such functions. Namely, their Reeb graphs are path or cycle graphs; any path graph, and any cycle graph with an even number of vertices, is isomorphic to the Reeb...
Morse-Sard theorem in infinite dimensional Banach spaces and investigation of the set of all critical levels