Lecture Notes on Mean Curvature Flow

By Carlo Mantegazza. 2011

280 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/831f5854672197af25bbe61495b69d0f11921827

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

In Geometry and Topology

Citations in the corpus

A general regularity theory for weak mean curvature flow (2011, background): “A good reference on the subject is [12], where one can find many useful estimates for Brakke’s flow written in smooth setting, and we mention [4, 10, 16, 20, 25, 37] and the references therein on the MCF.”
On the mean curvature flow of grain boundaries (2015, background): “Since the 1970’s, the MCF has been studied by numerous researchers as it is one of the fundamental geometric evolution problems (see [5, 14, 15, 24, 36] for the overview and references related to the MCF) appearing in fields such as differential geometry, general relativity, image processing and mat”
Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, background): “Some references are McDuff and Salamon [52] for symplectic geometry, the author [42] and Harvey and Lawson [27] for Calabi–Yau m-folds and special Lagrangians, Mantegazza [50], Smoczyk [67] and Neves [56] for (Lagrangian) MCF, Fukaya [18, 19], Fukaya, Oh, Ohta and Ono [20] and Seidel [64] for Lagran”
Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature (2018, background): “Indeed, it is sufficient to run the MCF starting at Σ for short time (see [56] for an account about the classical existence theory), say until some time ε0 > 0.”
The Ricci-Bourguignon Flow (2015, unknown): “In [Catino and Mantegazza 2011] the authors compute the evolution equation of the Weyl tensor during the Ricci ﬂow (see [Catino et al. 2015a] for a signiﬁcant application of this formula) and we use most of their computations.”