Geometry & Topology Volume 23, issue 1 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Other MSP Journals

(Log-)epiperimetric inequality and regularity over smooth cones for almost area-minimizing currents

Max Engelstein, Luca Spolaor and Bozhidar Velichkov

Geometry & Topology 23 (2019) 513–540

DOI: 10.2140/gt.2019.23.513

Bibliography

1	D Adams, L Simon, Rates of asymptotic convergence near isolated singularities of geometric extrema, Indiana Univ. Math. J. 37 (1988) 225 MR963501
2	W K Allard, F J Almgren Jr., On the radial behavior of minimal surfaces and the uniqueness of their tangent cones, Ann. of Math. 113 (1981) 215 MR607893
3	T H Colding, W P Minicozzi II, Uniqueness of blowups and Łojasiewicz inequalities, Ann. of Math. 182 (2015) 221 MR3374960
4	M Colombo, L Spolaor, B Velichkov, Direct epiperimetric inequalities for the thin obstacle problem and applications, preprint (2017) arXiv:1709.03120
5	M Colombo, L Spolaor, B Velichkov, A logarithmic epiperimetric inequality for the obstacle problem, Geom. Funct. Anal. 28 (2018) 1029 MR3820438
6	C De Lellis, E Spadaro, L Spolaor, Uniqueness of tangent cones for two-dimensional almost-minimizing currents, Comm. Pure Appl. Math. 70 (2017) 1402 MR3666570
7	M Engelstein, L Spolaor, B Velichkov, Uniqueness of the blow-up at isolated singularities for the Alt–Caffarelli functional, preprint (2018) arXiv:1801.09276
8	S Łojasiewicz, Ensembles semi-analytiques, IHES (1965)
9	T Nagura, On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres, III, Osaka J. Math. 19 (1982) 241 MR667489
10	E R Reifenberg, An epiperimetric inequality related to the analyticity of minimal surfaces, Ann. of Math. 80 (1964) 1 MR0171197
11	R Schoen, L Simon, A new proof of the regularity theorem for rectifiable currents which minimize parametric elliptic functionals, Indiana Univ. Math. J. 31 (1982) 415 MR652826
12	L Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. 118 (1983) 525 MR727703
13	L Simon, Lectures on geometric measure theory, 3, Australian National University (1983) MR756417
14	J E Taylor, Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 in R³, Invent. Math. 22 (1973) 119 MR0333903
15	J E Taylor, The structure of singularities in solutions to ellipsoidal variational problems with constraints in R³, Ann. of Math. 103 (1976) 541 MR0428182
16	B White, Tangent cones to two-dimensional area-minimizing integral currents are unique, Duke Math. J. 50 (1983) 143 MR700134