$L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifolds

Details $L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifolds $L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifolds

2005-09-11

arxiv.org/abs/math/0509237v1

GEOMETRIAE DEDICATA,119(2006)151-158

Mathematics

Differential Geometry

11 pages

Scientific paper

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 with compact support is non-increasing along the Ricci flow with bounded curvature. The $L^{\infty}$ norm is showed to have monotonicity property too. Then we use $L^{\infty}$ 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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