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L p harmonic 1 -form on submanifold with weighted Poincaré inequality

Xiaoli Chao, Yusha Lv (2018)

Czechoslovak Mathematical Journal

We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is δ -stable or has sufficiently small total curvature, we establish two vanishing theorems for L p harmonic 1 -forms, which are extensions of the results of Dung-Seo and Cavalcante-Mirandola-Vitório.

L p , q -cohomology of warped cylinders

Yaroslav Kopylov (2009)

Annales mathématiques Blaise Pascal

We extend some results by Gol dshtein, Kuz minov, and Shvedov about the L p -cohomology of warped cylinders to L p , q -cohomology for p q . As an application, we establish some sufficient conditions for the nontriviality of the L p , q -torsion of a surface of revolution.

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