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Volumn 23, Issue 9-10, 1998, Pages 1475-1492

An example of three dimensional fattening for linked space curves evolving by curvature

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EID: 0040579517     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309808821392     Document Type: Article
Times cited : (9)

References (31)
  • 1
    • 0000147123 scopus 로고
    • Mean curvature flow through singularities for surfaces of rotation
    • S. Altschuler, S. Angenent, and Y. Giga. Mean curvature flow through singularities for surfaces of rotation. J. Geom. Anal., 5, pages 293-358, 1995.
    • (1995) J. Geom. Anal. , vol.5 , pp. 293-358
    • Altschuler, S.1    Angenent, S.2    Giga, Y.3
  • 2
    • 84972538842 scopus 로고
    • Singularities of the curve shrinking flow for space curves
    • S. J. Altschuler. Singularities of the curve shrinking flow for space curves. J. Differential Geom., 34, pages 491-514, 1991.
    • (1991) J. Differential Geom. , vol.34 , pp. 491-514
    • Altschuler, S.J.1
  • 3
    • 0040779974 scopus 로고    scopus 로고
    • Lecture notes on geometric evolution problems, distance function and viscosity solutions
    • Springer-Verlag, to appear
    • L. Ambrosio. Lecture notes on geometric evolution problems, distance function and viscosity solutions. In Proc. of the School on Calculus of Variations, Pisa 1996. Springer-Verlag, to appear.
    • Proc. of the School on Calculus of Variations, Pisa 1996
    • Ambrosio, L.1
  • 4
    • 0006528348 scopus 로고    scopus 로고
    • A level set approach to the evolution of surfaces of any codimension
    • L. Ambrosio and H.-M. Soner. A level set approach to the evolution of surfaces of any codimension. J. Differential Geom., 43, pages 693-737, 1996.
    • (1996) J. Differential Geom. , vol.43 , pp. 693-737
    • Ambrosio, L.1    Soner, H.-M.2
  • 5
    • 0001315015 scopus 로고
    • Parabolic equations for curves and surfaces part I. Curves with p-integrable curvature
    • S. Angenent. Parabolic equations for curves and surfaces part I. Curves with p-integrable curvature. Ann. Math., 132, pages 451-483, 1990.
    • (1990) Ann. Math. , vol.132 , pp. 451-483
    • Angenent, S.1
  • 6
    • 0001315014 scopus 로고
    • Parabolic equations for curves and surfaces part II. Intersections, blow-up and generalized solutions
    • S. Angenent. Parabolic equations for curves and surfaces part II. Intersections, blow-up and generalized solutions. Ann. Math., 133, pages 171-215, 1991.
    • (1991) Ann. Math. , vol.133 , pp. 171-215
    • Angenent, S.1
  • 11
    • 0009143376 scopus 로고    scopus 로고
    • Minimal barriers for geometric evolutions
    • G. Bellettini and M. Novaga. Minimal barriers for geometric evolutions. J. Differential Eqs., 139, pages 76-103, 1997.
    • (1997) J. Differential Eqs. , vol.139 , pp. 76-103
    • Bellettini, G.1    Novaga, M.2
  • 12
    • 0009138906 scopus 로고    scopus 로고
    • Comparison results between minimal barriers and viscosity solutions for geometric evolutions
    • G. Bellettini and M. Novaga. Comparison results between minimal barriers and viscosity solutions for geometric evolutions. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), XXVI, pages 97-131, 1998.
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.26 , pp. 97-131
    • Bellettini, G.1    Novaga, M.2
  • 13
    • 0040779975 scopus 로고    scopus 로고
    • A result on motion by mean curvature in arbitrary codimension
    • to appear
    • G. Bellettini and M. Novaga. A result on motion by mean curvature in arbitrary codimension. Diff. Geom. and its Appl., (to appear).
    • Diff. Geom. and Its Appl.
    • Bellettini, G.1    Novaga, M.2
  • 16
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y.-G. Chen, Y. Giga, and S. Goto. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom., 33, pages 749-786, 1991.
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.-G.1    Giga, Y.2    Goto, S.3
  • 18
    • 0040779970 scopus 로고
    • New ideas in calculus of variations and geometric meaasure theory
    • Walter De Gruyter, Berlin
    • E. De Giorgi. New ideas in calculus of variations and geometric meaasure theory. In Motion by Mean Curvature and Related Topics, Trento, pages 63-69. Walter De Gruyter, Berlin, 1992.
    • (1992) Motion by Mean Curvature and Related Topics, Trento , pp. 63-69
    • De Giorgi, E.1
  • 22
    • 0001673425 scopus 로고
    • Interior estimates for hypersurfaces moving by mean curvature
    • K. Ecker and G. Huisken. Interior estimates for hypersurfaces moving by mean curvature. Invent. Math., 103, pages 547-569, 1991.
    • (1991) Invent. Math. , vol.103 , pp. 547-569
    • Ecker, K.1    Huisken, G.2
  • 23
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature I
    • L.C. Evans and J. Spruck. Motion of level sets by mean curvature I. J. Differential Geom., 33, pages 635-681, 1991.
    • (1991) J. Differential Geom. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 24
    • 0039594273 scopus 로고    scopus 로고
    • Numerical evidence of fattening for the mean curvature flow
    • F. Fierro and M. Paolini. Numerical evidence of fattening for the mean curvature flow. Math. Models Methods Appl. Sci., 6, pages 793-813, 1996.
    • (1996) Math. Models Methods Appl. Sci. , vol.6 , pp. 793-813
    • Fierro, F.1    Paolini, M.2
  • 25
    • 84963023423 scopus 로고
    • The heat equation shrinking convex plane curves
    • M.E. Gage and R.S. Hamilton. The heat equation shrinking convex plane curves. J. Differential Geom., 23, pages 69-96, 1986.
    • (1986) J. Differential Geom. , vol.23 , pp. 69-96
    • Gage, M.E.1    Hamilton, R.S.2
  • 26
    • 84972528479 scopus 로고
    • The heat equation shrinks embedded plane curves to round points
    • M. A. Grayson. The heat equation shrinks embedded plane curves to round points. J. Differential Geom., 26, pages 285-314, 1987.
    • (1987) J. Differential Geom. , vol.26 , pp. 285-314
    • Grayson, M.A.1
  • 27
    • 84972507688 scopus 로고
    • Flow by mean curvature of convex surfaces into spheres
    • G. Huisken. Flow by mean curvature of convex surfaces into spheres. J. Differential Geom., 20, pages 237-266, 1984.
    • (1984) J. Differential Geom. , vol.20 , pp. 237-266
    • Huisken, G.1
  • 28
    • 0002635872 scopus 로고
    • Generalized flow of sets by mean curvature on a manifold
    • T. Ilmanen. Generalized flow of sets by mean curvature on a manifold. Indiana Univ. Math. J., 41, pages 671-705, 1992.
    • (1992) Indiana Univ. Math. J. , vol.41 , pp. 671-705
    • Ilmanen, T.1
  • 29
    • 0026895714 scopus 로고
    • Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter
    • M. Paolini and C. Verdi. Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter. Asymptotic Anal., 5, pages 553-574, 1992.
    • (1992) Asymptotic Anal. , vol.5 , pp. 553-574
    • Paolini, M.1    Verdi, C.2
  • 30
    • 0001283493 scopus 로고
    • Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature
    • H.-M. Soner and P.E. Souganidis. Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature. Comm. Partial Differential Equations, 18, pages 859-894, 1993.
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 859-894
    • Soner, H.-M.1    Souganidis, P.E.2
  • 31
    • 0039594274 scopus 로고
    • Some questions of De Giorgi about mean curvature flow of triply-periodic surfaces
    • Walter De Gruyter, Berlin
    • B. White. Some questions of De Giorgi about mean curvature flow of triply-periodic surfaces. In Motion by Mean Curvature and Related Topics, Trento, pages 210-213. Walter De Gruyter, Berlin, 1992.
    • (1992) Motion by Mean Curvature and Related Topics, Trento , pp. 210-213
    • White, B.1


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