* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
This work is devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.
Regularity Theory for Mean Curvature Flow
This book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory.
We study Brakke's motion of varifolds by mean curvature in the special case that the initial surface is an integral cycle, giving a new existence proof by mean of elliptic regularization.
This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010.
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities.
This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized.
In Surveys in geometric analysis and relativity, vol. 20 of Adv. Lect. Math. (ALM). Int. Press, Somerville, MA, 2011, pp. 73–143. [5] M , J. Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, ...
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop.
1985, D. Hoffman and W. Meeks, [HoMe1], proved that Costa's surface was embedded; this surface is now known as the Costa-Hoffman-Meeks surface. Moreover, Hoffman and Meeks showed that Costa's surface was just the first in a family of ...