Zobrazeno 1 - 10
of 265
pro vyhledávání: '"Topping, Peter"'
Autor:
Sobnack, Arjun, Topping, Peter M.
Given two disjoint nested embedded closed curves in the plane, both evolving under curve shortening flow, we show that the modulus of the enclosed annulus is monotonically increasing in time. An analogous result holds within any ambient surface satis
Externí odkaz:
http://arxiv.org/abs/2409.03098
Autor:
Sobnack, Arjun, Topping, Peter M.
Given two curves bounding a region of area $A$ that evolve under curve shortening flow, we propose the principle that the regularity of one should be controllable in terms of the regularity of the other, starting from time $A/\pi$. We prove several r
Externí odkaz:
http://arxiv.org/abs/2408.04049
Autor:
Topping, Peter M.
We survey several problems concerning Riemannian manifolds with positive curvature of one form or another. We describe the PIC1 notion of positive curvature and argue that it is often the sharp notion of positive curvature to consider. Finally we exp
Externí odkaz:
http://arxiv.org/abs/2309.00596
Autor:
Peachey, Luke T., Topping, Peter M.
The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a conformal factor. This led to the discovery of a
Externí odkaz:
http://arxiv.org/abs/2307.05306
Autor:
Topping, Peter M., Yin, Hao
In previous work we established the existence of a Ricci flow starting with a Riemann surface coupled with a nonatomic Radon measure as a conformal factor. In this paper we prove uniqueness. Combining these two works yields a canonical smoothing of s
Externí odkaz:
http://arxiv.org/abs/2306.08398
Autor:
Lee, Man-Chun, Topping, Peter M.
Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton. In this pa
Externí odkaz:
http://arxiv.org/abs/2211.07623