Enclosure theorems and barrier principles for energy stationary currents and the associated Brakke-flow

References

[1] J. Bemelmans and U. Dierkes, On a singular variational integral with linear growth. I. Existence and regularity of minimizers, Arch. Ration. Mech. Anal. 100 (1987), no. 1, 83–103. 10.1007/BF00281248Suche in Google Scholar

[2] R. Böhme, S. Hildebrandt and E. Tausch, The two-dimensional analogue of the catenary, Pacific J. Math. 88 (1980), no. 2, 247–278. 10.2140/pjm.1980.88.247Suche in Google Scholar

[3] K. A. Brakke, The Motion of a Surface by its Mean Curvature, Math. Notes 20, Princeton University Press, Princeton, 1978. Suche in Google Scholar

[4] U. Dierkes, Maximum principles and nonexistence results for minimal submanifolds, Manuscripta Math. 69 (1990), no. 2, 203–218. 10.1007/BF02567919Suche in Google Scholar

[5] U. Dierkes, A Bernstein result for energy minimizing hypersurfaces, Calc. Var. Partial Differential Equations 1 (1993), no. 1, 37–54. 10.1007/BF02163263Suche in Google Scholar

[6] U. Dierkes, S. Hildebrandt and A. J. Tromba, Regularity of Minimal Surfaces, 2nd ed., Grundlehren Math. Wiss. 340, Springer, Heidelberg, 2010. 10.1007/978-3-642-11700-8Suche in Google Scholar

[7] U. Dierkes and G. Huisken, The n-dimensional analogue of the catenary: Existence and nonexistence, Pacific J. Math. 141 (1990), no. 1, 47–54. 10.2140/pjm.1990.141.47Suche in Google Scholar

[8] U. Dierkes and D. Schwab, Maximum principles for submanifolds of arbitrary codimension and bounded mean curvature, Calc. Var. Partial Differential Equations 22 (2005), no. 2, 173–184. 10.1007/s00526-004-0270-0Suche in Google Scholar

[9] K. Ecker, Local techniques for mean curvature flow, Workshop on Theoretical and Numerical Aspects of Geometric Variational Problems (Canberra 1990), Proc. Centre Math. Appl. Austral. Nat. Univ. 26, Australian National University, Canberra (1991), 107–119. Suche in Google Scholar

[10] P. Henkemeyer, Erschließungs- und nichtexistenzsätze in der geometrischen maßtheorie, Dissertation, Universität Duisburg–Essen, 2017. Suche in Google Scholar

[11] P. Henkemeyer, Enclosure and non-existence theorems for area stationary currents and currents with mean curvature vector, preprint. 10.1007/s00013-020-01461-4Suche in Google Scholar

[12] S. Hildebrandt, Maximum principles for minimal surfaces and for surfaces of continuous mean curvature, Math. Z. 128 (1972), 253–269. 10.1007/BF01111709Suche in Google Scholar

[13] T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108 (1994), no. 520, 1–90. 10.1090/memo/0520Suche in Google Scholar

[14] A. Lahiri, Regularity of the Brakke flow, Ph.D. thesis, Freie Universtität Berlin, 2014. Suche in Google Scholar

[15] L. Simon, Lectures on Geometric Measure Theory, Proc. Centre Math. Appl. Austral. Nat. Univ. 3, Australian National University, Canberra, 1983. Suche in Google Scholar

[16] A. Stone, Evolutionary existence proofs for the pendant drop and n-dimensional catenary problems, Pacific J. Math. 164 (1994), no. 1, 147–178. 10.2140/pjm.1994.164.147Suche in Google Scholar

[17] S. Winklmann, Maximum principles for energy stationary hypersurfaces, Analysis (Munich) 26 (2006), no. 2, 251–258. 10.1524/anly.2006.26.2.251Suche in Google Scholar