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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 22
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 2, April 2015
  4. Fully nonlinear curvature flow of axially symmetric hypersurfaces
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 6, December 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 5, October 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 4, August 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 3, June 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 2, April 2015
Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder’s estimates for a degenerate parabolic problem with dynamic boundary conditions
Minimal energy solutions for cooperative nonlinear Schrödinger systems
Linear and nonlinear eigenvalue problems for Dirac systems in unbounded domains
Large time behavior of solutions to degenerate parabolic equations
Liouville type theorem for higher-order elliptic system with Navier boundary condition
Fully nonlinear curvature flow of axially symmetric hypersurfaces
Nonlinear Differential Equations and Applications NoDEA : Volume 22, Issue 1, February 2015
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Fully nonlinear curvature flow of axially symmetric hypersurfaces

Content Provider SpringerLink
Author McCoy, James A. Wheeler, Valentina Mira Mofarreh, Fatemah Y. Y.
Copyright Year 2014
Abstract Recently, fully nonlinear curvature flow of a certain class of axially symmetric hypersurfaces with boundary conditions time of existence was obtained, in the case of convex speeds (J. A. McCoy et al., Annali di Matematica Pura ed Applicata 1–13, 2013). In this paper we remove the convexity condition on the speed in the case it is homogeneous of degree one in the principal curvatures and the boundary conditions are pure Neumann. Moreover, we classify the singularities of the flow of a larger class of axially symmetric hypersurfaces as Type I. Our approach to remove the convexity requirement on the speed is based upon earlier work of Andrews for evolving convex surfaces (B. H. Andrews, Invent Math 138(1):151–161, 1999; Calc Var Partial Differ Equ 39(3–4):649–657, 2010); these arguments for obtaining a ‘curvature pinching estimate’ may be adapted to this setting due to axial symmetry. As further applications of curvature pinching in this setting, we show that closed, convex, axially symmetric hypersurfaces contract under the flow to round points, and hypersurfaces contracting self-similarly are necessarily spheres. These results are new for n ≥ 3.
Ending Page 343
Page Count 19
Starting Page 325
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 2
Volume Number 22
Language English
Publisher Springer Basel
Publisher Date 2014-10-04
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Parabolic partial differential equation Hypersurface Geometric evolution equations (mean curvature flow, Ricci flow, etc.) Nonlinear initial value problems for linear parabolic equations Analysis Neumann boundary condition Curvature flow Initial-boundary value problem Free boundary problems Nonlinear parabolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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