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Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, a
Externí odkaz:
http://arxiv.org/abs/2404.12755
In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\"ahler-Ricci soliton on $\mathbb{C}^{n}$ and asked whether every steady gradient K\"ahler-Ricci soliton of positive curvature on $\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (a
Externí odkaz:
http://arxiv.org/abs/2403.04089
A noncollapsed $\mathbb{F}$-limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of $\mathbb{F}$-convergence [Bam20a,Bam20b,Bam20c]. In this article, we shall present a systematic
Externí odkaz:
http://arxiv.org/abs/2401.03387
Autor:
Chan, Pak-Yeung, Lee, Man-Chun
In this work, we show that complete non-compact manifolds with non-negative Ricci curvature, Euclidean volume growth and sufficiently small curvature concentration are necessarily flat Euclidean space.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2312.07845
We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an earlier result in [CDM22] to higher dimensions. In dimension four, we cl
Externí odkaz:
http://arxiv.org/abs/2310.14020
The metric flow is introduced and extensively studied by Bamler [Bam20b, Bam20c], especially as an $\mathbb{F}$-limit of a sequence of smooth Ricci flows with uniformly bounded Nash entropy, in which case each regular point on the limit is a point of
Externí odkaz:
http://arxiv.org/abs/2310.14007
Autor:
Chan, Pak-Yeung, Lee, Man-Chun
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence theory witho
Externí odkaz:
http://arxiv.org/abs/2305.01396
Autor:
Li, Haiwei, Zhao, Yongling, Bardhan, Ronita, Chan, Pak-Wai, Derome, Dominique, Luo, Zhiwen, Urge-Vorsatz, Diana, Carmeliet, Jan
Rising demand for space cooling has been placing enormous strain on various technological, environmental, and societal dimensions, resulting in issues related to energy consumption, environmental sustainability, health and well-being, affordability,
Externí odkaz:
http://arxiv.org/abs/2301.11565
We prove a local gap theorem for Ricci shrinkers, which states that if the local $\mu$-functional at scale $1$ on a large ball centered at the minimum point of the potential function is close enough to $0$, then the shrinker must be the flat gaussian
Externí odkaz:
http://arxiv.org/abs/2212.09203
Autor:
Tam, Cheuk Yin1, Chan, Pak Ho1, Cheng, Minerva Yuk Yee1, Lau, Adrian Ka Chun1, Tam, Kwan Kin1, Cheng, Tsz Ho1, So, Ho1 h99097668@hotmail.com
Publikováno v:
Journal of Clinical Rheumatology & Immunology (JCRI). Jul2024, Vol. 24 Issue 1, p34-40. 7p.