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Lagrangian self-similar solutions in gradient shrinking Kähler–Ricci solitons

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Abstract

In this paper, we give a lower bound estimate for the diameter of a Lagrangian self-shrinker in a gradient shrinking Kähler–Ricci soliton as an analog of a result of Futaki et al. (Ann Global Anal Geom 44(2):105–114, 2013) for a self-shrinker in a Euclidean space. We also prove an analog of a result of Cao and Li (Calc Var Partial Differ Equ 46(3–4):879–889, 2013) about the non-existence of compact self-expanders in a Euclidean space.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Hikaru Yamamoto

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  1. Hikaru Yamamoto
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Correspondence to Hikaru Yamamoto.

Additional information

This work was supported by Grant-in-Aid for JSPS Fellows Grant Number 13J06407 and the Program for Leading Graduate Schools, MEXT, Japan.

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Yamamoto, H. Lagrangian self-similar solutions in gradient shrinking Kähler–Ricci solitons. J. Geom. 108, 247–254 (2017). https://doi.org/10.1007/s00022-016-0336-0

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  • DOI: https://doi.org/10.1007/s00022-016-0336-0

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