The Sobolev--Poincar 'e Inequality and the L_q,p-Cohomology of\n Twisted Cylinders

2019/04/22 by Vladimir Gol’dshtein, Gol'dshtein, Vladimir, Yaroslav Kopylov +1
Mathematics · #46E30 #55N05 #58A12 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1904.09914

openalex publication_date 2019/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a vanishing result for the L_q,p-cohomology (q\≥ p) of a\ntwisted cylinder, which is a generalization of a warped cylinder. The result is\nnew even for warped cylinders. We base on the methods for proving the (p,q)\nSobolev--Poincar 'e inequality developed by L.~Shartser.\n

Citations

• Twisted products in pseudo-Riemannian geometry
• A curvature condition for a twisted product¶to be a warped product

Related

• L_p,q-Cohomology of Warped Cylinders
• Reduced L_q,p-Cohomology of Some Twisted Products
• Some Sobolev-type inequalities for twisted differential forms on real and complex manifolds
• Twisted cohomology
• Generalized twisted coHom objects