Noncompact RCD(0,N) spaces with linear volume growth

Abstract

Since non-compact RCD(0, N) spaces have at least linear volume growth, we study noncompact RCD(0, N) spaces with linear volume growth in this paper. One of the main results is that the diameter of level sets of a Busemann function grow at most linearly on a noncompact RCD(0, N) space satisfying the linear volume growth condition. Another main result in this paper is a splitting theorem at the noncompact end for a RCD(0, N) space with strongly minimal volume growth. These results generalize some theorems on noncompact manifolds with nonnegative Ricci curvature to non-smooth settings.

arXiv commentIn this version, we add a new result on the growth of the diameter of level sets of Busemann functions on noncompact RCD(0, N) spaces. In addition, we drop the non-branching assumption on the splitting type theorem. There are some adjustment on the structure of the paper. All comments are welcome!

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• Metric measure spaces with Riemannian Ricci curvature bounded from below
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• Sharp Spectral Gaps on Metric Measure Spaces

Cited by in corpus (1)

• An almost rigidity Theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth