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arXiv · 1812.11764

Hodge decomposition of the Sobolev space $H^1$ on a space form of nonpositive curvature

Chi Hin Chan·Magdalena Czubak·Carlos Pinilla Suarez
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Abstract

The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and $L^2$ forms. We further extend the Hodge decomposition to the Sobolev space $H^1$ for general $k$-forms on non-compact manifolds of nonpositive constant sectional curvature. As a result, we also obtain a decomposition on $\mathbb R^N$.

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Chi Hin Chan, Magdalena Czubak, Carlos Pinilla Suarez. 2018-12-31. Hodge decomposition of the Sobolev space $H^1$ on a space form of nonpositive curvature. https://arxiv.org/abs/1812.11764

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