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arxiv: 1812.11764 · v1 · pith:N7U2LQN3new · submitted 2018-12-31 · 🧮 math.DG · math.AP

Hodge decomposition of the Sobolev space H¹ on a space form of nonpositive curvature

Chi Hin Chan , Magdalena Czubak , Carlos Pinilla Suarez This is my paper
classification 🧮 math.DG math.AP
keywords decompositionhodgemanifoldsspacecurvatureformsnon-compactnonpositive
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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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