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Former Research Group

Geometric Measure Theory and Applications - Publications

Explore the scholarly works of the "Geometric Measure Theory and Applications" group. Browse journal articles, contributions in books and conference proceedings, academic theses, or discover our research through preprints.

inJournal
2019 Repository Open Access
Camillo De Lellis, Antonio De Rosa and Francesco Ghiraldin

A direct approach to the anisotropic Plateau problem

In: Advances in calculus of variations, 12 (2019) 2, pp. 211-223
BibTex DOI: 10.1515/acv-2016-0057 ArXiv: 1602.08757
inJournal
2018 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Regularity theory for 2-dimensional almost minimal currents I : Lipschitz approximation

In: Transactions of the American Mathematical Society, 370 (2018) 3, pp. 1783-1801
BibTex DOI: 10.1090/tran/6995 ArXiv: 1508.05507 MiS Preprint
inJournal
2018 Repository Open Access
Guido De Philippis, Antonio De Rosa and Francesco Ghiraldin

Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies

In: Communications on pure and applied mathematics, 71 (2018) 6, pp. 1123-1148
BibTex DOI: 10.1002/cpa.21713 ArXiv: 1609.01908 MiS Preprint
inJournal
2017 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Uniqueness of tangent cones for two-dimensional almost-minimizing currents

In: Communications on pure and applied mathematics, 70 (2017) 7, pp. 1402-1421
BibTex DOI: 10.1002/cpa.21690 ArXiv: 1508.05266 MiS Preprint
inJournal
2017 Repository Open Access
Paul Feehan

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

In: Journal of differential equations, 263 (2017) 5, pp. 2481-2553
BibTex DOI: 10.1016/j.jde.2017.04.003 ArXiv: 1302.1849 MiS Preprint
inJournal
2017 Repository Open Access
Matteo Focardi, Francesco Geraci and Emanuele Spadaro

The classical obstacle problem for nonlinear variational energies

In: Nonlinear analysis / A, 154 (2017), pp. 71-87
BibTex DOI: 10.1016/j.na.2016.10.020 ArXiv: 1610.09827
inJournal
2017 Repository Open Access
Francesco Ghiraldin and Luca Spolaor

On the number of singular points for planar multivalued harmonic functions

In: Manuscripta mathematica, 154 (2017) 3/4, pp. 513-525
BibTex DOI: 10.1007/s00229-017-0920-0 ArXiv: 1601.01967 MiS Preprint
inJournal
2017 Repository Open Access
Andrea Mondino and Emanuele Spadaro

On an isoperimetric-isodiametric inequality

In: Analysis and PDE, 10 (2017) 1, pp. 95-126
BibTex DOI: 10.2140/apde.2017.10.95 ArXiv: 1603.05263 MiS Preprint
inJournal
2016 Repository Open Access
Giovanni Alberti and Andrea Marchese

On the differentiability of Lipschitz functions with respect to measures in the Euclidean space

In: Geometric and functional analysis, 26 (2016) 1, pp. 1-66
BibTex DOI: 10.1007/s00039-016-0354-y ArXiv: 1408.2379 MiS Preprint
inJournal
2016 Repository Open Access
Panagiota Daskalopoulos and Paul Feehan

C1,1 regularity for degenerate elliptic obstacle problems

In: Journal of differential equations, 260 (2016) 6, pp. 5043-5074
BibTex DOI: 10.1016/j.jde.2015.11.037 ArXiv: 1206.0831 MiS Preprint
inJournal
2016 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Regularity of area minimizing currents II : center manifold

In: Annals of mathematics, 183 (2016) 2, pp. 499-575
BibTex DOI: 10.4007/annals.2016.183.2.2 ArXiv: 1306.1191 MiS Preprint
inJournal
2016 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Regularity of area minimizing currents III : blow-up

In: Annals of mathematics, 183 (2016) 2, pp. 577-617
BibTex DOI: 10.4007/annals.2016.183.2.3 ArXiv: 1306.1194 MiS Preprint
inJournal
2016 Repository Open Access
Matteo Focardi and Emanuele Spadaro

An epiperimetric inequality for the thin obstacle problem

In: Advances in differential equations, 21 (2016) 1/2, pp. 153-200
BibTex ArXiv: 1502.07168 MiS Preprint Link: projecteuclid.org
Academic
2016 Repository Open Access
Philippe Logaritsch

An obstacle problem for mean curvature flow

Dissertation, Universität Leipzig, 2016
BibTex Link: nbn-resolving.de
inJournal
2016 Repository Open Access
Andrea Marchese and Annalisa Massaccesi

An optimal irrigation network with infinitely many branching points

In: Control, optimisation and calculus of variations (ESAIM-COCV), 22 (2016) 2, pp. 543-561
BibTex DOI: 10.1051/cocv/2015028 ArXiv: 1408.2406 MiS Preprint
inJournal
2016 Repository Open Access
Andrea Marchese and Annalisa Massaccesi

The Steiner tree problem revisited through rectifiable G-currents

In: Advances in calculus of variations, 9 (2016) 1, pp. 19-39
BibTex DOI: 10.1515/acv-2014-0022 ArXiv: 1408.2696 MiS Preprint
inJournal
2016 Journal Open Access
Luca Mugnai, Christian Seis and Emanuele Spadaro

Global solutions to the volume-preserving mean-curvature flow

In: Calculus of variations and partial differential equations, 55 (2016) 1, p. 18
BibTex DOI: 10.1007/s00526-015-0943-x ArXiv: 1502.07232 MiS Preprint
inJournal
2015 Repository Open Access
Katarína Bellová and Fanghua Lin

Nodal sets of Steklov eigenfunctions

In: Calculus of variations and partial differential equations, 54 (2015) 2, pp. 2239-2268
BibTex DOI: 10.1007/s00526-015-0864-8 ArXiv: 1402.4323 MiS Preprint
inJournal
2015 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Multiple valued functions and integral currents

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 14 (2015) 4, pp. 1239-1269
BibTex DOI: 10.2422/2036-2145.201306_002 ArXiv: 1306.1188 MiS Preprint
Preprint
2015 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Regularity theory for 2-dimensional almost minimal currents III : blowup

BibTex ArXiv: 1508.05510 MiS Preprint
inJournal
2015 Repository Open Access
Paul Feehan and Camelia Pop

Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

In: Advances in differential equations, 20 (2015) 3-4, pp. 361-432
BibTex ArXiv: 1208.2658 MiS Preprint Link: projecteuclid.org
inJournal
2015 Repository Open Access
Matteo Focardi, Andrea Marchese and Emanuele Spadaro

Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result

In: Journal of functional analysis, 268 (2015) 11, pp. 3290-3325
BibTex DOI: 10.1016/j.jfa.2015.02.011 ArXiv: 1409.2320 MiS Preprint
inJournal
2015 Repository Open Access
Matteo Focardi, Emanuele Spadaro and Maria Stella Gelli

Monotonicity formulas for obstacle problems with Lipschitz coefficients

In: Calculus of variations and partial differential equations, 54 (2015) 2, pp. 1547-1573
BibTex DOI: 10.1007/s00526-015-0835-0 ArXiv: 1306.2127 MiS Preprint
inJournal
2015 Repository Open Access
Matteo Focardi, Paolo Maria Mariano and Emanuele Spadaro

Multi-value microstructural descriptors for complex materials : analysis of ground states

In: Archive for rational mechanics and analysis, 217 (2015) 3, pp. 899-933
BibTex DOI: 10.1007/s00205-015-0846-1 Link: www.researchgate.net
inJournal
2015 Repository Open Access
Bernd Kirchheim, Emanuele Spadaro and László Székelyhidi

Equidimensional isometric maps

In: Commentarii mathematici Helvetici, 90 (2015) 4, pp. 761-798
BibTex DOI: 10.4171/CMH/370 ArXiv: 1408.6737 MiS Preprint
inJournal
2015 Repository Open Access
Andrea Marchese

On the building dimension of closed cones and Almgren's stratification principle

In: Proceedings of the American Mathematical Society, 143 (2015) 7, pp. 3041-3046
BibTex DOI: 10.1090/S0002-9939-2015-12497-5 ArXiv: 1408.2398 MiS Preprint
inJournal
2014 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Regularity of area minimizing currents I : gradient Lp estimates

In: Geometric and functional analysis, 24 (2014) 6, pp. 1831-1884
BibTex DOI: 10.1007/s00039-014-0306-3 ArXiv: 1306.1195 MiS Preprint
inJournal
2014 Repository Open Access
Paul Feehan and Camelia Pop

Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

In: Journal of differential equations, 256 (2014) 3, pp. 895-956
BibTex DOI: 10.1016/j.jde.2013.08.012 ArXiv: 1210.6727 MiS Preprint
inJournal
2014 Repository Open Access
Philippe Logaritsch and Andrea Marchese

Kirszbraun's extension theorem fails for Almgren's multiple valued functions

In: Archiv der Mathematik, 102 (2014) 5, pp. 455-458
BibTex DOI: 10.1007/s00013-014-0642-4 ArXiv: 1408.2426 MiS Preprint
inBook
2014 Repository Open Access
Emanuele Spadaro

Regularity of higher codimension area minimizing integral currents

In: Geometric measure theory and real analysis / Luigi Ambrosio (ed.)
Edizioni della Normale : Pisa, 2014. - pp. 131-192
(Publications of the Scuola Normale Superiore / CRM series ; 17)
BibTex DOI: 10.1007/978-88-7642-523-3_3 ArXiv: 1501.03720 Link: www.mis.mpg.de
inJournal
2013 Repository Open Access
Marco Cicalese and Emanuele Spadaro

Droplet minimizers of an isoperimetric problem with long-range interactions

In: Communications on pure and applied mathematics, 66 (2013) 8, pp. 1298-1333
BibTex DOI: 10.1002/cpa.21463 ArXiv: 1110.0031 MiS Preprint
inJournal
2012 Repository Open Access
Philippe Logaritsch and Emanuele Spadaro

A representation formula for the p-energy of metric space-valued Sobolev maps

In: Communications in contemporary mathematics, 14 (2012) 6, p. 1250043
BibTex DOI: 10.1142/S0219199712500435 ArXiv: 1112.0122 MiS Preprint
Preprint
2012 Repository Open Access
Emanuele Spadaro

Mean-convex sets and minimal barriers

BibTex ArXiv: 1112.4288 MiS Preprint
inJournal
2012 Repository Open Access
Emanuele Spadaro

Nondoubling A∞ weights

In: Advances in calculus of variations, 5 (2012) 3, pp. 345-354
BibTex DOI: 10.1515/acv.2011.019 Link: personal-homepages.mis.mpg.de
inJournal
2011 Repository Open Access
Emanuele Spadaro and Camillo De Lellis

On Almgren's center manifold and regularity of minimal surfaces [In: Partial differential equations ; August 7th - August 13th, 2011 ; report no. 38/2011]

In: Oberwolfach reports, 8 (2011) 3, pp. 2187-2188
BibTex DOI: 10.4171/OWR/2011/38 Link: publications.mfo.de