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On Lower Volume Growth Estimate for f-Minimal Submanifolds in Gradient Shrinking Soliton

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Wei, Yong

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Duke University Press

Abstract

Let (Mm,g¯,f) be a complete gradient shrinking soliton with convex potential f. We show that any complete noncompact properly immersed f-minimal submanifold Σn in Mm must have at least linear volume growth. This is a Calabi–Yau type volume growth estimate.

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International Mathematics Research Notices

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Restricted until

2099-12-31
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