Komplexní vesmír Rogera Penrose
We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is -stable or has sufficiently small total curvature, we establish two vanishing theorems for harmonic -forms, which are extensions of the results of Dung-Seo and Cavalcante-Mirandola-Vitório.
We extend some results by Goldshtein, Kuzminov, and Shvedov about the -cohomology of warped cylinders to -cohomology for . As an application, we establish some sufficient conditions for the nontriviality of the -torsion of a surface of revolution.
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.