Výsledky vyhledávání - "Xie, Junming"

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Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature

This is a sequel to our paper [24], in which we investigated the geometry of 4-dimensional gradient shrinking Ricci solitons with half positive (nonnegative) isotropic curvature. In this paper, we mainly focus on 4-dimensional gradient steady Ricci s

Externí odkaz: http://arxiv.org/abs/2403.19627

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Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$

Autor: Xie, Junming, Yu, Jiangtao

Publikováno v: J. Geom. Anal. 33 (2023), no. 8, Paper No. 252, 19 pp

In this paper, inspired by the work of Spruck-Xiao [27] and based partly on a result of Derdzi\'nski [11], we prove the convexity of complete 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$. More precisely

Externí odkaz: http://arxiv.org/abs/2211.14281

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Four-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature

Autor: Cao, Huai-Dong, Xie, Junming

Publikováno v: Math. Z. 305 (2023), no. 2, Paper No. 25, 22 pp

In this paper, we investigate the geometry of 4-dimensional complete gradient shrinking Ricci solitons with half positive isotropic curvature (half PIC) or half nonnegative isotropic curvature. Our first main result is a certain form of curvature est

Externí odkaz: http://arxiv.org/abs/2211.09091

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Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio

Autor: Cao, Huai-Dong, Liu, Tianbo, Xie, Junming

Publikováno v: Calc. Var. Partial Differential Equations, 62 (2023), no. 2, Paper No. 48, 19 pp

Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $ \limsup_{r\to \infty} R

Externí odkaz: http://arxiv.org/abs/2203.13178

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