, Handbook of mathematical functions Isoperimetric curves on hyperbolic surfaces, Proc. Amer. Math. Soc., to appear 2003. [Alm] F. Almgren, Existence and Regularity almost everywhere of Solutions to Elliptic Variational Problems with constraints, p.165, 1965.
, Séminaire de probabilités XIX Lévy-Gromov Isoperimetric Inequality for an infinite- Dimensional Diffusion Generator, Sur les inégalités de Sobolev logarithmiques. Société Mathématique de France Bakry, L'Hypercontractivité et son Utilisation en Théorie des Semigroupes. Lectures on Probability Theory (Saint-Flour, 1992), Lecture Notes in Math. 1581BQ2] D. Bakry & Z. Qian, Volume compararison theorems without Jacobi fields. [Ba1] F. Barthe, Extremal Properties of Central Half-Spaces for Product MeasuresBa2] F. Barthe, Log-concave and spherical models in isoperimetry. Geometric And Functional Analysis, pp.1-114, 1983.
, Some remarks on isoperimetry of gaussian type, Annales de l'Institut H. Poincaré Probabilités et Statistiques, pp.419-434, 2000.
, Isoperimetric Comparison Theorems for Convex Bodies En préparation, Ann. Scient. Ec. Norm. Sup, vol.49, pp.479-490, 1986.
, A new isoperimetric comparison theorem for surfaces of variable curvature Spectral geometry: direct and inverse problem. With appendixes by G From vanishing theorems to estimating theorems : the Bochner technique revisited, Duke Mathematical Journal Besson. Lecture Notes in Mathematics Bulletin of the American Mathematical Society, vol.85, issue.19 2, pp.359-396, 1986.
, Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov, Invent. math, vol.80, pp.295-308, 1985.
, Inégalités isopérimétriques pour l'´ equation de la chaleur et applicationàapplication`applicationà l'estimation de quelques invariants. Séminaire Goulaouic-Meyer- Schwartz, Inégalités isopérimétriques et applications, pp.513-542, 1982.
, Extremal Properties of Half-spaces for Log-Concave Distributions. The Annals of Probability, pp.35-48, 1996.
, Isoperimetric and analytic inequalities for log-concave probability measures. The Annals of Probability Some connections between isoperimetric and Sobolevtype inequalities. Memoirs of the Isoperimetric Constants for Product Probability Measures. The Annals of Probability, Number Bobkov & C. Houdré, vol.27, issue.25, pp.184-205, 1903.
, Isoperimetrische Ungleichung für Bereiche auf Flächen, Jber. Deutsch. Math.-Verein, vol.51, pp.219-257, 1941.
, Regularity theory for almost minimal currents, Arch. Res. Mech. Anal, vol.78, pp.99-130, 1982.
, A Course in Metric Geometry Geometric Inequalities. A series of Comprehensive Studies in Mathematics 285 On Cheeger's Inequality ? 1 h 2 /4, in Geometry of the Laplace Operator [C1] I. Chavel, Riemannian Geometry : a modern introduction [C2] I. Chavel, Isoperimetric Inequalities, Proceedings of Symposia in Pure MathematicsCa] G. Carron, Inégalités isopérimétriques sur les variétés riemanniennes Thèse de doctorat de Mathématiques de l'Université Joseph Fourier Cheeger, A lower bound for the smallest eigenvalue of the Laplacian. Problems in Analysis, A Symposium in Honour of Salomon Bochner Differentiability of Lipschitz functions on metric measure spaces, pp.29-77, 1914.
, Lower bounds on the Ricci curvature and the almost rigidity of warped products On the Structure of Spaces with Ricci curvature bounded below.I On the Structure of Spaces with Ricci curvature bounded below.II, ChC1] J. Cheeger & T. H. ColdingChC2] J. Cheeger & T. H. ColdingChC3] J. Cheeger & T. H. Colding, On the Structure of Spaces with Ricci curvature bounded below.III. Journal of Differential Geometry, pp.189-237, 1996.
, Comparison Theorems in Riemannian Geometry Cheng, Eigenvalue comparison theorems and its geometric applications, C1] T. H. Colding, Shape of manifolds with positive Ricci curvature. Invent. Math, pp.289-297, 1975.
, Large manifolds with positive Ricci curvature, Inventiones Mathematicae, vol.124, issue.1-3, pp.193-214, 1996.
DOI : 10.1007/s002220050050
, Ricci Curvature and Volume Convergence, The Annals of Mathematics, vol.145, issue.3, pp.477-501, 1997.
DOI : 10.2307/2951841
, The isoperimetric problem on some singular surfaces
, Isopérimétrie pour les groupes et les variétés Courtois, Spectrum of Manifolds with holes, Revista Mathemática Iberoamericana Journal of Functional Analysis, vol.9, issue.134, pp.293-314, 1993.
, Croke, A sharp four dimensional isoperimetric inequality [Dv] A. Dvoretzki, Some results on convex bodies and Banach spaces, Proc. Symp. on Linear Spaces Druet, Sharp Local Isoperimetric Inequalities involvig the Scalar Curvature. Proceedings of theE1] J. H. Eshenburg, Comparison theorems and hypersurfaces. Manuscripta math. 59E2] J. H. Eshenburg, Comparison theory for Riccati equations. Manuscripta math, pp.253-256, 1961.
, Geometric Measure Theory Normal and Integral Currents, Ann. Math, vol.72, pp.458-520, 1960.
, Leprobì eme des isopérimètres sur les surfaces ouvertesàouvertes`ouvertesà courbure positive, Comment. Math. Helv, vol.1341, pp.293-346, 1940.
DOI : 10.1007/bf01378068
, The dimension of almost spherical sections of convex bodies, Acta Mathematica, vol.139, issue.0, pp.52-94, 1977.
DOI : 10.1007/BF02392234
, Collapsing of Riemannian Manifolds and Eigenvalues of Laplace operator, Invent. Math, vol.87, pp.517-547, 1987.
, Upper Bounds for the First Eigenvalue of the Laplace-Beltrami Operator, Indiana Univ. Math. J, vol.29, pp.897-912, 1980.
, Inégalités isopérimétriques et analytiques sur les variétés riemanniennes Société mathématique de France, Astérisque 163-164 Isoperimetric inequalities based on integral norms of Ricci curvature. Société mathématique de France, Astérisque 157-158, G3] S. Gallot, Volumes, courbure de Ricci et convergence des variétés. Séminaire Bourbaki, 50ème année, pp.31-91, 1988.
, On the regularity of boundaries of sets minimizing perimeter with a volume constraint Large soap bubles and isoperimetric regions in the product of euclidean space with a closed manifold Stuctures métriques pour les variétés riemanniennes Paul Levy's Isoperimetric Inequality. Appendix C in Metric Structures for Riemannian and non Riemannian Spaces by M.Gromov, Birkhäuser. [G02] M. Gromov, Isoperimetry of waists and concentration of maps, Metric Structures for Riemannian and Non-Riemannian Spaces. Birkhäuser, 1999. [Gr1] M. Gromov, pp.25-37, 1978.
, The Isoperimetric problem on surfaces. The American Mathematical Montly, Pincements du ? 1 et diamètre. Annales de l'Institut Fourier Kleiner, An isoperimetric comparison theorem. Inventiones Mathematicae, pp.843-863, 1992.
, The Geometry of Domains in space, Birkhäuser Advanced texts, Inégalités isopérimétriques en analyse et probabilités. Séminaire Bourbaki, 45ème année, pp.343-375, 1993.
, The Concentration of Measure Phenomenon Mathematical Surveys and Monographs Probability in Banach Spaces, Probì emes concrets d'analyse fonctionnelle. Gauthier-Villars, 1951.
, Mattila, Geometry of Sets and Measure in Euclidean Spaces, Fractals and Rectifiability, Maz'ya, Sobolev SpacesMi0] V. D. Milman, New proof of the theorem of Dvoretzky on sections of convex bodies, pp.865-883, 1971.
, Asymptotic theory of Finite Dimensional Normed Spaces Geometric measure theory, a beginner's guide, M1] F. Morgan, Regularity of isoperimetric Hypersurfaces in Riemannian Manifolds. Transactions of the AMS, pp.5041-5052, 1200.
, Area-minimizing surfaces in cones, Communications in Analysis and Geometry, vol.10, issue.5, pp.971-983, 2002.
DOI : 10.4310/CAG.2002.v10.n5.a3
, Small Balls about Some Vertex Minimize Perimeter The Isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Transactions of The, pp.4889-4909, 2000.
, Some sharp isoperimetric theorems for Riemannian manifolds, Indiana University Mathematics Journal, vol.49, issue.3, pp.1017-1041, 2000.
DOI : 10.1512/iumj.2000.49.1929
, The Isoperimetric Inequality Bulletin of the Sur la régularité du profil isopérimétrique des surfaces riemanniennes compactes Annales de l'Institut Fourier Profil isopérimétrique, métriques périodiques et formes d'´ equilibre des cristaux ESAIM: Control, Optimization and Calculus of Variations The isoperimetric problem in spherical cylinders Isoperimetric domains in the Riemanniann Product of a Circle with a simply connected Space Form and A pplications to Free Boundary Problem, Isoperimetric regions in cones. Trans. Amer. Math. Soc.. [P2] P. Pansu The Isoperimetric Problem in Complete Surfaces of Non-Negative Curvature, pp.2327-2339, 1975.
, Stable constant mean curvature tori and the isoperimetric problem in three space forms, Commentarii Mathematici Helvetici, vol.67, issue.1, pp.293-305, 1992.
DOI : 10.1007/BF02566501
, The isoperimetric problem Lecture series given during the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces at the MSRI, Isopérimétrie fonctionnelle dimensionnelle en courbure positive. Comptes Rendus de l'Académie des Sciences de Paris, pp.251-254, 2000.
, A new proof of the regularity theorem for rectifiable currents which minimize parametric elliptic functionals, Indiana Univ. Math. J, vol.31, pp.184-193, 1982.
, Die Brunn-Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie, Math. Nach. 1, pp.81-157, 1948.
, On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint, Comm. Anal. Geom, vol.7, issue.1, pp.199-220, 1999.
, Lectures on Geometric Measure Theory [Ti] Titchmarsh, The theory of functions, Proceedings of the Centre for Mathematical Analysis Toponogov, Riemannian spaces having their curvature bounded below by a positive number. Uspehi Mat. Nauk, pp.87-130, 1932.
, Sur les surfacesàsurfaces`surfacesà courbure négative, C. R. Acad. Sci, vol.182, pp.1069-1071, 1926.
, Weakly differentiable functions, Sobolev spaces and functions of bounded variation, 1989.
, Propriétés de concavité du profil isopérimétrique et applications, Thèse de Doctorat, 2003.
, A Differential Inequality for the Isoperimetric Profile, Int. Math. Res. Not
, Sur une in???galit??? isop???rim???trique qui g???n???ralise celle de Paul L???vy-Gromov, Inventiones Mathematicae, vol.11, issue.2, pp.295-30858017, 1985.
DOI : 10.1007/BF01388608
, In??galit??s isop??rim??triques et applications, Annales scientifiques de l'??cole normale sup??rieure, vol.15, issue.3, pp.513-541, 1982.
DOI : 10.24033/asens.1435
, Regularity theory for almost minimal currents MR MR83i:49077 [Ch] Isaac Chavel, Eigenvalues in Riemannian geometry Riemannian Geometry: a modern introduction MR MR95j:53001 [Ch3] , Isoperimetric Inequalities. Differential Geometric and Analytic Perspectives, [Ga] Sylvestre Gallot, Inégalités isopérimétriques et analytiques sur les variétés riemanniennes Minimal surfaces and functions of bounded variation, pp.169-1723154, 1974.
, MR 84d:49043 [Gr] Misha Gromov, Paul Lévy's Isoperimetric Inequality, Appendix C in Metric Structures for Riemannian and non Riemannian Spaces by M. Gromov Boundary regularity for solutions of a partitioning problem Optimal regularity for codimension one minimal surfaces with a free boundary A beginner's guide, MR 88m:49032 262 BIBLIOGRAPHIE [K] Ernst Kuwert, Note on the Isoperimetric Profile of a Convex Body, personal communication. [M1] Frank Morgan, Geometric measure theory Regularity of isoperimetric hypersurfaces in Riemannian manifolds, pp.25-37, 1983.
, Some sharp isoperimetric theorems for Riemannian manifolds, Indiana University Mathematics Journal, vol.49, issue.3, pp.1017-1041, 2000.
DOI : 10.1512/iumj.2000.49.1929
URL : http://doi.org/10.1512/iumj.2000.49.1929
, Isoperimetric regions in cones, Transactions of the American Mathematical Society, vol.354, issue.06, pp.2327-233953089, 2002.
DOI : 10.1090/S0002-9947-02-02983-5
, Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones, Trans. Amer. Math. Soc
, The isoperimetric problem, Lecture series given during the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces at the MSRI, 2001.
, Stability for hypersurfaces of constant mean curvature with free boundary, Geometriae Dedicata, vol.160, issue.1, pp.19-33, 1995.
DOI : 10.1007/BF01263611
, Connectivity of Phase Boundaries in Strictly Convex Domains, Archive for Rational Mechanics and Analysis, vol.141, issue.4, pp.375-400, 1998.
DOI : 10.1007/s002050050081
, Weakly differentiable functions Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics MR, vol.120, issue.91, p.46046, 1989.