Generic mean curvature flow I; generic singularities
نویسندگان
چکیده
منابع مشابه
Marangoni-driven singularities via mean-curvature flow
In this work, it is demonstrated that the existence and topology of the recently observed interfacial singularities driven by Marangoni effects can be deduced using mean-curvature flow theory extended to account for variations of interfacial tension. This suggests that some of the physical mechanisms underlying the formation of these interfacial singularities may originate from/be modeled by th...
متن کاملSingularities of Lagrangian Mean Curvature Flow: Monotone Case
We study the formation of singularities for the mean curvature flow of monotone Lagrangians in C. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When n = 2, we can improve this result by showing that connected components of the rescaled flow converge to an a...
متن کاملSingularities of Lagrangian Mean Curvature Flow: Zero-maslov Class Case
We study singularities of Lagrangian mean curvature flow in C when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonian isotopic to a plane that, nevertheless, develop finite time singularities under ...
متن کاملMean Curvature Blowup in Mean Curvature Flow
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.
متن کاملGeneral Curvature Flow without Singularities
In [5], Sáez and Schnürer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature flow. In this paper, we generalize their results to a general curvature setting. Our key ingredient is the existence result of general curvature flow with bounda...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.175.2.7