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V. Bögelein, F. Duzaar, N. Fusco (2015)
A sharp quantitative isoperimetric inequality in higher codimensionRendiconti Lincei-matematica E Applicazioni, 26
B. Reichardt (2007)
Proof of the Double Bubble Conjecture in RnJournal of Geometric Analysis, 18
V. Bögelein, F. Duzaar, Christoph Scheven (2015)
A sharp quantitative isoperimetric inequality in hyperbolic n-spaceCalculus of Variations and Partial Differential Equations, 54
A. Cianchi, N. Fusco, F. Maggi, A. Pratelli (2011)
On the isoperimetric deficit in Gauss spaceAmerican Journal of Mathematics, 133
(1984)
Conference on linear partial and pseudodifferential operators (Torino, 1982)
D. Prandi, L. Rizzi, M. Seri (2015)
A sub-Riemannian Santal\'o formula with applications to isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic operators
E. Giusti (1977)
Minimal surfaces and functions of bounded variation
N. Garofalo, D. Nhieu (1996)
ISOPERIMETRIC AND SOBOLEV INEQUALITIES FOR CARNOT-CARATHEODORY SPACES AND THE EXISTENCE OF MINIMAL SURFACESCommunications on Pure and Applied Mathematics, 49
Roberto Monti (2008)
Heisenberg isoperimetric problem. The axial case, 1
T. O’Neil (2002)
Geometric Measure Theory
V Bögelein, F Duzaar, N Fusco (2015)
A sharp quantitative isoperimetric inequality in higher codimensionAtti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 26
J Foisy, M Alfaro, J Brock, N Hodges, J Zimba (1993)
The standard double soap bubble in $${ R}^2$$ R 2 uniquely minimizes perimeterPac. J. Math., 159
R. Monti, Daniele Morbidelli (2004)
Isoperimetric inequality in the Grushin planeThe Journal of Geometric Analysis, 14
M. Cicalese, G. Leonardi (2010)
A Selection Principle for the Sharp Quantitative Isoperimetric InequalityArchive for Rational Mechanics and Analysis, 206
Manuel Ritor'e (2008)
A proof by calibration of an isoperimetric inequality in the Heisenberg group H^narXiv: Differential Geometry
BY Almgren, F. Almgren (1975)
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraintsBulletin of the American Mathematical Society, 81
R. Monti, Matthieu Rickly (2006)
Convex isoperimetric sets in the Heisenberg groupAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 8
Manuel Ritor'e, César Rosales (2005)
Area-stationary surfaces in the Heisenberg group H1Advances in Mathematics, 219
V Franceschi, GP Leonardi, R Monti (2015)
Quantitative isoperimetric inequalities in $$\mathbb{H}^n$$ H nCalc. Var. Partial Differ. Equ., 54
F. Morgan (1988)
Geometric Measure Theory: A Beginner's Guide
F. Maggi (2012)
Sets of Finite Perimeter and Geometric Variational Problems: Equilibrium shapes of liquids and sessile drops
L. Capogna, D. Danielli, N. Garofalo (1994)
The geometric Sobolev embedding for vector fields and the isoperimetric inequalityCommunications in Analysis and Geometry, 2
E Giusti (1984)
Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics
F. Maggi (2012)
Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory
V Franceschi, R Monti (2016)
Isoperimetric problem in $$H$$ H -type groups and Grushin spacesRev. Mat. Iberoam., 32
A. Figalli, F. Maggi, A. Pratelli (2010)
A mass transportation approach to quantitative isoperimetric inequalitiesInventiones mathematicae, 182
M. Ritoré, César Rosales (2005)
Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group ℍnThe Journal of Geometric Analysis, 16
Valentina Franceschi (2016)
Sharp and Quantitative Isoperimetric Inequalities in Carnot-Carathéodory spaces
M Hutchings, F Morgan, M Ritoré, A Ros (2002)
Proof of the double bubble conjectureAnn. Math., 155
B. Franchi, S. Gallot, R. Wheeden (1994)
Sobolev and isoperimetric inequalities for degenerate metricsMathematische Annalen, 300
(1996)
Meyers–Serrin type theorems and relaxation of variational integrals depending vector fields
Xinhe Zhu (2011)
On the Isoperimetric Inequality in the Heisenberg Group2011 International Conference on Control, Automation and Systems Engineering (CASE)
Joel Foisy, M. Alfaro, J. Brock, Nickelous Hodges, J. Zimba (1993)
The standard double soap bubble in R2 uniquely minimizes perimeterPacific Journal of Mathematics, 159
N. Fusco, F. Maggi, A. Pratelli (2008)
The sharp quantitative isoperimetric inequalityAnnals of Mathematics, 168
FJ Almgren (1976)
Existence and regularity almost everywhere of solutions to elliptic variational problems with constraintsMem. Am. Math. Soc., 165
R Monti, M Rickly (2009)
Convex isoperimetric sets in the Heisenberg groupAnn. Sc. Norm. Super. Pisa Cl. Sci. (5), 8
F. Morgan (2000)
Proof of the Double Bubble ConjectureThe American Mathematical Monthly, 108
(1982)
Une métrique associée à une classe d'opérateurs elliptiques dégénérés
Valentina Franceschi, R. Monti (2014)
Isoperimetric problem in H-type groups and Grushin spacesarXiv: Optimization and Control
B. Franchi, C. Gutiérrez, R. Wheeden (1994)
Weighted Sobolev-Poincaré inequalities for Grushin type operatorsCommunications in Partial Differential Equations, 19
We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose three prescribed areas in the Grushin plane, using the least amount of perimeter, under an additional “one-dimensional” constraint on the intersections of their boundaries. We prove existence of regular solutions for this problem, and we characterize them in terms of isoperimetric sets, showing differences with the Euclidean case. The problem arises from the study of quantitative isoperimetric inequalities and has connections with the theory of minimal clusters.
Calculus of Variations and Partial Differential Equations – Springer Journals
Published: Jul 8, 2017
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