Classification of limiting shapes for isotropic curve flows

By Ben Andrews. 2002

176 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/652e5ba0095332054e61273c7f1c46914a3557e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yiming Zhao
2. Qi-Rui Li
3. Yong Huang
4. Haodi Chen
5. Shibing Chen
6. K. Boroczky
7. Dongmeng Xi
8. Guangxian Zhu

In Computational Mechanics

1. Guangxian Zhu
2. Yiming Zhao
3. Shibing Chen
4. Qi-Rui Li
5. Yong Huang
6. Paul Bryan
7. M. Jiang
8. Jiakun Liu

In Mathematical Physics

1. Guangxian Zhu
2. Qi-Rui Li
3. Shibing Chen
4. Yiming Zhao
5. Yong Huang
6. Haodi Chen
7. Paul Bryan
8. M. Jiang

Citations in the corpus

• The dual Minkowski problem for negative indices (2017, background): “The logarithmic Minkowski problem has strong connections with whether a measure has an affine isotropic image (Böröczky-LYZ [10]) and curvature flows (Andrews [2, 3]).”
• The discrete logarithmic Minkowski problem (2014, background): “, [2, 3, 13, 16, 34, 35]), and have important applications to Sobolev-type inequalities (see, e.”
• The logarithmic Minkowski problem for polytopes (2014, methodology): “measure on S(1), homothetic solutions to isotropic flows (classified by Andrews [3]) are solutions of the Lp Minkowski problem.”
• Variations of a class of Monge–Ampère-type functionals and their applications (2021, background): “4) when α > 1 n+2 [1, 2, 8], which makes our paper self-contained.”
• Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem (2009, methodology): “Either of these arguments can be used to deduce Grayson’s theorem, by making use of previous results concerning the classification of singularities: If the maximum curvature remains comparable to that of a circle with the same extinction time, Huisken’s monotonicity formula [11] implies that the cur”
• On the planar dual Minkowski problem (2018, methodology): “This is because the equation describes the self-similar solution of curve shortening flow, and by Gage-Hamilton’s Theorem [23] it must be a circle; see also [5, 9, 24, 32].”
• The Minkowski problem in Gaussian probability space (2020, background): “The logarithmic Minkowski problem has strong connections with isotropic measures (Böröczky-LutwakYang-Zhang [14]) and curvature flows (Andrews [1, 2]).”
• Existence of solutions to the even dual Minkowski problem (2018, background): “The logarithmic Minkowski problem has strong connections with isotropic measures (Böröczky-LYZ [10]), curvature flows (Andrews [2, 3]), and the log-Brunn-Minkowski inequality (Böröczky-LYZ [8], Colesanti, Livshyts & Marsiglietti [15], Rotem [52], Saroglou [53]), an inequality stronger than the class”
• Remarks on the 2-Dimensional Lp-Minkowski Problem (2010, result): “We also refer to [4,5,9,10,14,21] for other existence results and [7] for the uniqueness.”
• Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in $$\mathbb{C}^n$$ (2006, unknown): “This has been proved for n = 1 by Abresch and Langer [1] and recently by Andrews [4]; computer experiments provide some evidence of this fact in higher dimension.”