Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 2, pp. 209-259.
@article{AIHPC_2002__19_2_209_0,
     author = {Lin, Fang Hua and Wang, Chang You},
     title = {Harmonic and quasi-harmonic spheres, part {III.} {Rectifiablity} of the parabolic defect measure and generalized varifold flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {209--259},
     publisher = {Elsevier},
     volume = {19},
     number = {2},
     year = {2002},
     mrnumber = {1902744},
     zbl = {1042.58006},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2002__19_2_209_0/}
}
TY  - JOUR
AU  - Lin, Fang Hua
AU  - Wang, Chang You
TI  - Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2002
SP  - 209
EP  - 259
VL  - 19
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPC_2002__19_2_209_0/
LA  - en
ID  - AIHPC_2002__19_2_209_0
ER  - 
%0 Journal Article
%A Lin, Fang Hua
%A Wang, Chang You
%T Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
%J Annales de l'I.H.P. Analyse non linéaire
%D 2002
%P 209-259
%V 19
%N 2
%I Elsevier
%U http://archive.numdam.org/item/AIHPC_2002__19_2_209_0/
%G en
%F AIHPC_2002__19_2_209_0
Lin, Fang Hua; Wang, Chang You. Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 2, pp. 209-259. http://archive.numdam.org/item/AIHPC_2002__19_2_209_0/

[1] Ambrosio L., Soner H.M., A measure-theoretic approach to higher codimension mean curvature flows (Dedicated to Ennio De Giorgi), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1-2) (1997) 27-49, (1998). | Numdam | MR | Zbl

[2] Ambrosio L., Soner H.M., Level set approach to mean curvature flow in arbitrary codimension, J. Differential Geom. 43 (4) (1996) 693-737. | MR | Zbl

[3] Almgren F.J., Q valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two, Bull. Amer. Math. Soc. (N.S.) 8 (2) (1983) 327-328. | MR | Zbl

[4] Almgren F.J., The Theory of Varifolds. Mimeographed Notes, Princeton, 1965.

[5] Allard W.K., An integrality theorem and a regularity theorem for surfaces whose first variation with respect to a parametric elliptic integrand is controlled, in: Geometric Measure Theory and the Calculus of Variations, Arcata, CA, 1984, Proc. Sympos. Pure Math., 44, American Mathematical Society, Providence, RI, 1986, pp. 1-28. | MR | Zbl

[6] Allard W.K., On the first variation of a varifold, Ann. of Math. (2) 95 (1972) 417-491. | MR | Zbl

[7] Bethuel F., On the singular set of stationary harmonic maps, Manu. Math. 78 (4) (1993) 417-443. | MR | Zbl

[8] Brakke K., The Motion of a Surface by its Mean Curvature, Mathematical Notes, 20, Princeton University Press, Princeton, NJ, 1978. | MR | Zbl

[9] Cheng X.X., Estimate of the singular set of the evolution problem for harmonic maps, J. Differential Geom. 34 (1) (1991) 169-174. | MR | Zbl

[10] Chen Y.M., Li J.Y., Lin F.H., Partial regularity for weak heat flows into spheres, Comm. Pure Appl. Math. 48 (4) (1995) 429-448. | MR | Zbl

[11] Chen Y.M., Lin F.H., Evolution of harmonic maps with Dirichlet boundary conditions, Comm. Anal. Geom. 1 (3-4) (1993) 327-346. | MR | Zbl

[12] Caffarelli L., Kohn R., Nirenberg L., Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (6) (1982) 771-831. | MR | Zbl

[13] Chen Y.M., Struwe M., Existence and partial regularity results for the heat flow for harmonic maps, Math. Z. 201 (1) (1989) 83-103. | MR | Zbl

[14] Ding W.Y., Tian G., Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom. 3 (3-4) (1995) 543-554. | MR | Zbl

[15] Eells J., Sampson J., Harmonic mappings of riemannian manifolds, Amer. J. Math. 86 (1964) 109-160. | MR | Zbl

[16] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR | Zbl

[17] Feldman M., Partial regularity for harmonic maps of evolution into spheres, Comm. Partial Differential Equations 19 (5-6) (1994) 761-790. | MR | Zbl

[18] Federer H., Ziemer W.P., The Lebesgue set of a function whose distribution derivatives are pth power summable, Indiana Univ. Math. J. 22 (1972/73) 139-158. | MR | Zbl

[19] Helein F., Regularite des applications faiblement harmoniques entre une surface et une variete riemannienne, C. R. Acad. Sci. Paris Ser. I Math. 312 (8) (1991) 591-596. | MR | Zbl

[20] Ilmanen T., Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature, J. Differential Geom. 38 (2) (1993) 417-461. | MR | Zbl

[21] Ilmanen T., Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108 (520) (1994). | MR | Zbl

[22] Jerrard R., Soner H.M., Scaling limits and regularity results for a class of Ginzburg-Landau systems, Ann. Inst. H. Poincaré Anal. Non Lineaire 16 (4) (1999) 423-466. | Numdam | MR | Zbl

[23] Lin F.H., Gradient estimates and blow-up analysis for stationary harmonic maps, Ann. of Math. (2) 149 (3) (1999) 785-829. | MR | Zbl

[24] Lin F.H., Mapping problems, fundamental groups and defect measures, Acta Math. Sin. (Engl. Ser.) 15 (1) (1999) 25-52. | MR | Zbl

[25] Lin F.H., Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds, Comm. Pure Appl. Math. 51 (4) (1998) 385-441. | MR | Zbl

[26] Lin F.H., Varifold type theory for Sobolev mappings, in: AMS/IP Stud. Adv. Math. 20, American Mathematical Society, Providence, RI, 2001, pp. 423-430. | MR | Zbl

[27] Lin F.H., Riviere T., Energy quantization for harmonic maps. Duke Math. J. (to appear). | MR | Zbl

[28] Lin F.H., Riviere T., A quantization property for static Ginzburg-Landau vortices, C.P.A.M. 54 (2) (2001) 206-228. | MR | Zbl

[29] Li J.Y., Tian G., Blow-up Locus for heat flows of harmonic maps, Acta Math. Sin. (Engl. Ser.) 16 (1) (2000) 29-62. | MR | Zbl

[30] Lin F.H., Wang C.Y., Energy identity of harmonic map flows from surfaces at finite singular time, Calc. Var. Partial Differential Equations 6 (4) (1998) 369-380. | MR | Zbl

[31] Lin F.H., Wang C.Y., Harmonic and quasi-harmonic spheres, Comm. Anal. Geom. 7 (2) (1999) 397-429. | MR | Zbl

[32] Lin F.H., Wang C.Y., Harmonic and quasi-harmonic spheres, Part II, Comm. Anal. Geom. (to appear). | MR | Zbl

[33] Simon L., Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. | MR | Zbl

[34] Simon L., Theorems on regularity and singularity of energy minimizing maps, Lectures in Mathematics ETH Zürichür, Birkhauser Verlag, Basel, 1996, (based on lecture notes by Norbert Hungerbhler). | MR | Zbl

[35] Struwe M., On the evolution of harmonic maps in higher dimensions, J. Differential Geom. 28 (3) (1988) 485-502. | MR | Zbl

[36] Struwe M., On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv. 60 (4) (1985) 558-581. | MR | Zbl

[37] White B., Stratification of minimal surfaces, mean curvature flows, and harmonic maps, J. Reine Angew. Math. 488 (1997) 1-35. | MR | Zbl

[38] Ziemer W.P., Weakly differentiable functions, Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics, 120, Springer-Verlag, New York, 1989. | MR | Zbl