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On an integral formula for differential forms and its applications on manifolds with boundary
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Gyula Csató
Published/Copyright:
December 10, 2013
Abstract
Given two k-forms α and β on a compact Riemannian manifold M with boundary ∂M, we derive an identity relating
to an integral on the boundary ∂M. Herein Fk is a bundle endomorphism depending only on the Riemannian curvature tensor. Essential is how the tangential and normal parts of α and β, respectively their derivatives, appear in the integrand of the boundary integral. The identity gives a very simple proof for many classical results, which require that α = β and also that the tangential part αT (or the normal part αN) vanishes on ∂M. Moreover we generalize some of the boundary conditions in Gaffney inequality and in nonexistence theorems for harmonic fields.
Received: 2013-4-24
Published Online: 2013-12-10
Published in Print: 2013-12-1
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Masthead
- The Cardon and Robert Criterion for the Riemann hypothesis
- Multiplications and convolutions in L. Schwartz' spaces of test functions and distributions and their continuity
- Delay difference equations: Coexistence of oscillatory and nonoscillatory solutions
- On an integral formula for differential forms and its applications on manifolds with boundary
- Some Hermite–Hadamard type inequalities for log-h-convex functions
- Asymptotic of some integral
- Argument properties of symmetric analytic functions
- Three new sequences converging to the Euler–Mascheroni constant
- Universality of multivariate interpolation
