A measure theoretic approach to higher codimension mean curvature flows
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 27-49.
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     author = {Ambrosio, Luigi and Soner, Halil Mete},
     title = {A measure theoretic approach to higher codimension mean curvature flows},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {27--49},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {1-2},
     year = {1997},
     mrnumber = {1655508},
     zbl = {1043.35136},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_1-2_27_0/}
}
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Ambrosio, Luigi; Soner, Halil Mete. A measure theoretic approach to higher codimension mean curvature flows. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 27-49. http://www.numdam.org/item/ASNSP_1997_4_25_1-2_27_0/

[1] W.K. Allard, On the first variation of a varifold, Ann. of Math. 95 (1972), 417-491. | MR | Zbl

[2] L. Ambrosio - H.M. Soner, Level set approach to mean curvature flow in any codimension, J. Diff. Geom. 43 (1996), 693-737. | MR | Zbl

[3] G. Barles - H.M. Soner - P.E. Souganidis, Front propagation and phase field theory, SIAM. J. Cont. Opt. 31 (1993), 439-469. | MR | Zbl

[4] G. Bellettini - M. Paolini, Some results on minimal barriers in the sense of De Giorgi applied to motion by mean curvature, Rend. Atti Accad. Naz. XL, XIX (1995), 43-67. | MR | Zbl

[5] G. Bellettini - M. Paolini, Teoremi di confronto tra diverse nozioni di movimento secondo la curvatura media, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Mat. App. 6 (1995), 45-54. | MR | Zbl

[6] G. Bellettini - M. Novaga, Comparison results between minimal barriers and viscosity solutions for geometric evolutions, submitted to Ann. Sc. Norm. Sup., (1996). | Numdam | Zbl

[7] F. Bethuel - H. Brezis - F. Helein, "Ginzburg-Landau vortices", Birkhäuser, Boston, 1994. | MR | Zbl

[8] K.A. Brakke, "The Motion of a Surface by its Mean Curvature", Princeton University Press, Princeton N. J., 1978. | MR | Zbl

[9] G. Buttazzo - L. Freddi, Functionals defined on measures and aplications to non equi-uniformly elliptic problems, Ann. Mat. Pura Appl. 159 (1991), 133-146. | MR | Zbl

[10] X. Chen, Generation and propagation of interfaces by reaction diffusion equation, J. Diff. Eqs. 96 (1992), 116-141. | MR | Zbl

[11] E. De Giorgi, Su una teoria generale della misura (r - 1)-dimensionale in uno spazio a r dimensioni, Ann. Mat. Pura Appl. Ser IV 36 (1954), 191-213. | MR | Zbl

[12] E. De Giorgi, Nuovi teoremi relativi alle misure (r - 1)-dimensionali in uno spazio a r dimensioni, Ric. Mat. 4 (1955), 95-113. | MR | Zbl

[13] E. De Giorgi, Some conjectures on flow by mean curvature, in "Proc. Capri Workshop 1990", Benevento-Bruno-Sbordone (eds.), 1990.

[14] E. De Giorgi, Barriers, boundaries, motion of manifolds, "Lectures held in Pavia", 1994.

[15] P. De Mottoni - M. Schatzman, Developments of interfaces in Rn, "Proc. Royal Soc. Edinburgh" 116A (1990), 207-220. | Zbl

[16] P. De Mottoni - M. Schatzman, Évolution géométriques d'interfaces, C.R. Acad. Sci. Paris Sér. I Math. 309 (1989), 453-458. | MR | Zbl

[17] L.C. Evans - H.M. Soner - P.E. Souganidis, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45 (1992), 1097-1123. | MR | Zbl

[18] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Diff. Geom. 20 (1984), 237-266. | MR | Zbl

[19] J.E. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimizing curvature, Indiana Univ. Math. J. 35 (1986), 45-71. | MR | Zbl

[20] T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature, J. Diff. Geom. 38 (1993), 417-461. | MR | Zbl

[21] T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Memoirs of AMS, Vol. 108, Number 520, (1994). | MR | Zbl

[22] R.L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals, preprint. | MR

[23] R.L. Jerrard - H.M. Soner, Scaling limits and regularity results for a class of Ginzburg-Landau systems, Ann. Inst. H. Poincaré, forthcoming. | Numdam | MR | Zbl

[24] R.L. Jerrard - H.M. Soner, Dynamics of Ginzburg-Landau vortices, Arch. Rat. Mech. An. forthcoming. | MR | Zbl

[25] F.H. Lin, Dynamics of Ginzburg-Landau vortices: the pinning effect, C.R. Acad. Sci. Paris 322 (1996), 625-630. | MR | Zbl

[26] F.H. Lin, Solutions of Ginzburg-Landau equations and critical points of renormalized energy, Ann. Inst. Henri Poincare 12 (1995), 599-622. | Numdam | MR | Zbl

[27] F.H. Lin, Some dynamical properties of Ginzburg-Landau votices, C.P.A.M. 49 (1996), 323-359. | MR | Zbl

[28] S. Müller, Mathematical models of microstructure and the Calculus of variations, preprint MPI Leipzig, 1997.

[29] L.M. Pismen - J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model, Physica D. 47 (1991), 353-360. | MR | Zbl

[30] Y. Reshetnyak, Weak convergence of completely additive functions on a set, Siberian Math. J. 9 (1968), 487-498.

[31] L. Simon, "Lectures on Geometric Measure Theory, Centre for Mathematical Analysis ", Australian National University, Canberra, 1984. | MR | Zbl

[32] H.M. Soner, Ginzburg-Landau equation and motion by mean curvature, I: convergence; II: development of the initial interface, J. Geometric Analysis (1993), to appear. | MR

[33] M. Struwe, On the asymptotic behaviour of minimizers of the Ginzburg-Landau model in 2 dimensions, Diff. and Int. Equations 7 (1994), 1613-1624. | MR | Zbl