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L 2 Forms and Ricci Flow with Bounded Curvature on Complete Non-Compact Manifolds

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Abstract

In this paper, we study the evolution of L 2 one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the L 2 norm of a smooth one form is non-increasing along the Ricci flow with bounded curvature. The L ∞ norm is showed to have monotonicity property too. Then we use L ∞ cohomology of one forms with compact support to study the singularity model for the Ricci flow on \(S^1\times\mathbb{R}^{n-1}\).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Li Ma & Yang Yang

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  1. Li Ma
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  2. Yang Yang
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Correspondence to Li Ma.

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Ma, L., Yang, Y. L 2 Forms and Ricci Flow with Bounded Curvature on Complete Non-Compact Manifolds. Geom Dedicata 119, 151–158 (2006). https://doi.org/10.1007/s10711-006-9064-1

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  • DOI: https://doi.org/10.1007/s10711-006-9064-1

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