## Morgan, Frank

Compute Distance To:
 Author ID: morgan.frank Published as: Morgan, Frank; Morgan, F. Homepage: http://math.williams.edu/morgan External Links: MGP · Wikidata
 Documents Indexed: 126 Publications since 1976, including 13 Books 2 Further Contributions Co-Authors: 56 Co-Authors with 45 Joint Publications 1,229 Co-Co-Authors
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### Co-Authors

 82 single-authored 5 Sullivan, John M. jun. 4 Hutchings, Michael Lounsbery 4 Ritoré, Manuel 3 Harvey, Reese 3 Ros, Antonio 2 Adams, Colin C. 2 Gluck, Herman 2 Hass, Joel 2 Howards, Hugh Nelson 2 Lawlor, Gary R. 1 Almgren, Robert F. 1 Bayle, Vincent 1 Bolton, Roger 1 Brakke, Kenneth A. 1 Bray, Hubert L. 1 Brothers, John E. 1 Burger, Edward B. 1 Cañete, Antonio 1 Carozza, Davide 1 Chung, Ping Ngai 1 Cook, Jack S. 1 Corwin, Ivan Z. 1 Cox, Steven J. 1 Dadok, Jiri 1 Epstein, David Bernard Alper 1 Fernández, Miguel Ángel 1 Forman, Robin 1 French, Christopher P. 1 Furedi, Zoltan 1 Graner, François 1 Greenleaf, Scott 1 Gulliver, Robert D. II 1 Hardt, Robert M. 1 Harman, Nate 1 Holmes, Thomas J. 1 Howe, Sean 1 Hsu, Wen-Tai 1 Johnson, David Lewis 1 Johnson, Stewart D. 1 Jones, B. Frank jun. 1 Kern, Norbert 1 Keyfitz, Barbara Lee 1 Kusner, Robert B. 1 Lagarias, Jeffrey C. 1 Larché, Francis 1 Li, Yifei 1 Lieb, Elliott Hershel 1 Lovett, Jonathan 1 Mackenzie, Dana Walter Nance 1 Mara, Michael Kelly 1 Marden, Albert 1 Maurmann, Quinn 1 Miller, Steven J. 1 Newkirk, Edward 1 Pansu, Pierre 1 Pedersen, Lori 1 Plata, Isamar Rosa 1 Pratelli, Aldo 1 Rosales, César 1 Salavessa, Isabel M. C. 1 Seferis, Deividas 1 Shah, Niralee 1 Sordo Vieira, Luis 1 Taylor, Jean Ellen 1 Wichiramala, Wacharin 1 Wikner, Elena 1 Wolf, Michael 1 Ziller, Wolfgang
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### Serials

 11 Proceedings of the American Mathematical Society 10 American Mathematical Monthly 9 Transactions of the American Mathematical Society 6 The Journal of Geometric Analysis 4 The Mathematical Intelligencer 4 Indiana University Mathematics Journal 4 Pacific Journal of Mathematics 3 Archive for Rational Mechanics and Analysis 3 Inventiones Mathematicae 3 Mathematische Annalen 3 Annals of Global Analysis and Geometry 2 Bulletin of the Australian Mathematical Society 2 Duke Mathematical Journal 2 Michigan Mathematical Journal 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Calculus of Variations and Partial Differential Equations 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Reviews of Modern Physics 1 Mathematics Magazine 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Commentarii Mathematici Helvetici 1 Journal of Differential Geometry 1 Journal of Economic Theory 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Revista Matemática Iberoamericana 1 International Journal of Mathematics 1 Aequationes Mathematicae 1 Communications in Partial Differential Equations 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Review 1 Experimental Mathematics 1 Communications in Analysis and Geometry 1 Electronic Research Announcements of the American Mathematical Society 1 Matemática Contemporânea 1 European Mathematical Society Newsletter 1 The Asian Journal of Mathematics 1 Annals of Mathematics. Second Series 1 Interfaces and Free Boundaries 1 Student Mathematical Library 1 Involve 1 São Paulo Journal of Mathematical Sciences 1 Analysis and Geometry in Metric Spaces 1 MAA Spectrum
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### Fields

 87 Calculus of variations and optimal control; optimization (49-XX) 83 Differential geometry (53-XX) 14 Convex and discrete geometry (52-XX) 14 Global analysis, analysis on manifolds (58-XX) 7 Measure and integration (28-XX) 6 General and overarching topics; collections (00-XX) 4 Real functions (26-XX) 4 Geometry (51-XX) 4 Mechanics of deformable solids (74-XX) 4 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Relativity and gravitational theory (83-XX) 3 Operations research, mathematical programming (90-XX) 3 Mathematics education (97-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

105 Publications have been cited 1,391 times in 810 Documents Cited by Year
Manifolds with density. Zbl 1118.53022
Morgan, Frank
2005
Geometric measure theory. A beginner’s guide. Zbl 0671.49043
Morgan, Frank
1988
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 4th ed. Zbl 1179.49050
Morgan, Frank
2009
On the isoperimetric problem in Euclidean space with density. Zbl 1126.49038
Rosales, César; Cañete, Antonio; Bayle, Vincent; Morgan, Frank
2008
Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020
Morgan, Frank; Johnson, David L.
2000
Proof of the double bubble conjecture. Zbl 1009.53007
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio
2002
Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Zbl 1063.49031
Morgan, Frank
2003
Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025
Morgan, Frank
2000
Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Zbl 0830.49028
Lawlor, Gary; Morgan, Frank
1994
Geometric measure theory. A beginner’s guide. 2nd ed. Zbl 0819.49024
Morgan, Frank
1995
Isoperimetric regions in cones. Zbl 0988.53028
Morgan, Frank; Ritoré, Manuel
2002
Existence of isoperimetric regions in $$\mathbb{R}^{n}$$ with density. Zbl 1263.49049
Morgan, Frank; Pratelli, Aldo
2013
The isoperimetric problem on surfaces. Zbl 1003.52011
Howards, Hugh; Hutchings, Michael; Morgan, Frank
1999
The isoperimetric theorem for general integrands. Zbl 0923.49019
Brothers, John E.; Morgan, Frank
1994
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. Zbl 1338.49089
Morgan, Frank
2016
Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002
Morgan, Frank
1994
Clusters minimizing area plus length of singular curves. Zbl 0805.49025
Morgan, Frank
1994
The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Zbl 0976.53082
Morgan, Frank; Hutchings, Michael; Howards, Hugh
2000
Hexagonal economic regions solve the location problem. Zbl 1026.90059
Morgan, Frank; Bolton, Roger
2002
The exterior algebra $$\Lambda ^ kR^ n$$ and area minimization. Zbl 0585.49029
Morgan, Frank
1985
On the singular structure of two-dimensional area minimizing surfaces in $${\mathbb{R}}^ n$$. Zbl 0549.49029
Morgan, Frank
1982
Manifolds with density and Perelman’s proof of the Poincaré conjecture. Zbl 1170.53001
Morgan, Frank
2009
Myer’s theorem with density. Zbl 1132.53306
Morgan, Frank
2006
The cone over the Clifford torus in $$R^ 4$$ is $$\Phi$$-minimizing. Zbl 0725.49013
Morgan, Frank
1991
An isoperimetric comparison theorem for Schwarzschild space and other manifolds. Zbl 0994.53029
Bray, Hubert; Morgan, Frank
2002
Riemannian geometry. A beginner’s guide. 2nd ed. Zbl 0911.53001
Morgan, Frank
1998
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0557.49022
Morgan, Frank
1983
Isoperimetric comparison theorems for manifolds with density. Zbl 1175.49042
Maurmann, Quinn; Morgan, Frank
2009
Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $$\nu$$. Zbl 0617.49019
Morgan, Frank
1986
Area-minimizing currents bounded by higher multiples of curves. Zbl 0541.49018
Morgan, Frank
1984
Area-minimizing surfaces, faces of Grassmannians, and calibrations. Zbl 0672.49028
Morgan, Frank
1988
Calibrations on $${\mathbb{R}}^ 8$$. Zbl 0666.49015
Dadok, J.; Harvey, R.; Morgan, F.
1988
Minimal surfaces, crystals, shortest networks, and undergraduate research. Zbl 0765.52015
Morgan, Frank
1992
In polytopes, small balls about some vertex minimize perimeter. Zbl 1132.49036
Morgan, Frank
2007
Open problems in soap bubble geometry. Zbl 0867.53009
Sullivan, John M.; Morgan, Frank
1996
Examples of unoriented area-minimizing surfaces. Zbl 0509.53007
Morgan, Frank
1984
The log-convex density conjecture. Zbl 1238.49062
Morgan, Frank
2011
Volume-minimizing cycles in Grassmann manifolds. Zbl 0837.53035
Gluck, Herman; Mackenzie, Dana; Morgan, Frank
1995
The standard double bubble is the unique stable double bubble in $$\mathbb{R}^2$$. Zbl 1003.53010
Morgan, Frank; Wichiramala, Wacharin
2002
Planar Wulff shape is unique equilibrium. Zbl 1071.49025
Morgan, Frank
2005
Stable constant-mean-curvature hypersurfaces are area minimizing in small $$L^1$$ neighborhoods. Zbl 1195.49055
Morgan, Frank; Ros, Antonio
2010
Riemannian geometry. A beginner’s guide. Zbl 0794.53001
Morgan, Frank
1993
The faces of the Grassmannian of 3-planes in $${\mathbb{R}}^ 7$$ (calibrated geometries on $${\mathbb{R}}^ 7)$$. Zbl 0556.53036
Harvey, Reese; Morgan, Frank
1986
Calibrated geometries in Grassmann manifolds. Zbl 0681.53039
Gluck, Herman; Morgan, Frank; Ziler, Wolfgang
1989
Almost every curve in $$R^3$$ bounds a unique area minimizing surface. Zbl 0378.49028
Morgan, Frank
1978
Geodesic nets on the $$2$$-sphere. Zbl 0871.53038
Hass, Joel; Morgan, Frank
1996
Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Zbl 1229.49046
Morgan, Frank; Howe, Sean; Harman, Nate
2011
Isoperimetric estimates in products. Zbl 1097.49027
Morgan, Frank
2006
$$(M,\varepsilon,\delta)$$-minimal curve regularity. Zbl 0804.49033
Morgan, Frank
1994
Size-minimizing rectifiable currents. Zbl 0645.49024
Morgan, Frank
1989
Immiscible fluid clusters in $${\mathbb{R}}^2$$ and $${\mathbb{R}}^3$$. Zbl 0967.49026
Morgan, Frank
1998
Lower semicontinuity of energy clusters. Zbl 0886.49016
Morgan, Frank
1997
Measures on spaces of surfaces. Zbl 0529.58031
Morgan, Frank
1982
The Levy-Gromov isoperimetric inequality in convex manifolds with boundary. Zbl 1149.53021
Morgan, Frank
2008
A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027
Morgan, Frank
1986
Surfaces minimizing area plus length of singular curves. Zbl 0816.49033
Morgan, Frank
1994
A smooth curve in $$R^4$$ bounding a continuum of area minimizing surfaces. Zbl 0338.53003
Morgan, Frank
1976
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0592.53004
Morgan, Frank
1986
Singularities of minimal surfaces and networks and related extremal problems in Minkowski space. Zbl 0762.49014
Füredi, Z.; Lagarias, J. C.; Morgan, F.
1991
Calibrations and new singularities in area-minimizing surfaces: A survey. Zbl 0721.53058
Morgan, Frank
1990
Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006
Lawlor, Gary; Morgan, Frank
1996
Rotation in a normed plane. Zbl 1140.51013
Cook, Jack; Lovett, Jonathan; Morgan, Frank
2007
Calibrations modulo $$\nu$$. Zbl 0618.49019
Morgan, Frank
1987
Area-minimizing surfaces in cones. Zbl 1035.58011
Morgan, Frank
2002
Wulff clusters in $$\mathbb{R}^2$$. Zbl 0934.49024
Morgan, Frank; French, Christopher; Greenleaf, Scott
1998
Isoperimetric curves on hyperbolic surfaces. Zbl 0992.53048
1999
The hexagonal honeycomb conjecture. Zbl 0932.49032
Morgan, Frank
1999
Proof of the double bubble conjecture. Zbl 0970.53009
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio
2000
Clusters with multiplicities in $$\mathbb R^2$$. Zbl 1108.49034
Morgan, Frank
2005
A round ball uniquely minimizes gravitational potential energy. Zbl 1066.70010
Morgan, Frank
2005
The comass ball in $$\Lambda ^ 3({\mathbb{R}}^ 6)^*$$. Zbl 0594.53045
Harvey, Reese; Morgan, Frank
1986
Geodesics and soap bubbles in surfaces. Zbl 0865.53009
Hass, Joel; Morgan, Frank
1996
Hexagonal surfaces of Kapouleas. Zbl 1117.53010
Morgan, Frank
2005
Isoperimetric pentagonal tilings. Zbl 1253.52009
Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Sordo Vieira, Luis; Wikner, Elena
2012
Proof of the double bubble conjecture. Zbl 0990.49029
Morgan, Frank
2001
Mathematicians, including undergraduates, look at soap bubbles. Zbl 0814.53002
Morgan, Frank
1994
Are large perimeter-minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular? Zbl 1371.74233
Cox, S. J.; Morgan, F.; Graner, F.
2013
Geometric measure theory and the proof of the double bubble conjecture. Zbl 1125.49033
Morgan, Frank; Ritoré, Manuel
2005
The symmetry group of a curve preserves a plane. Zbl 0489.53002
Gulliver, Robert; Morgan, Frank
1982
The Gauss-Bonnet formula on surfaces with densities. Zbl 1251.53002
Corwin, Ivan; Morgan, Frank
2011
When soap bubbles collide. Zbl 1183.52015
Adams, Colin; Morgan, Frank; Sullivan, John M.
2007
A smooth curve in $$R^ 3$$ bounding a continuum of minimal manifolds. Zbl 0453.49027
Morgan, Frank
1981
Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in $$\mathbb R^n$$. Zbl 1085.52501
Morgan, Frank
2005
Perimeter-minimizing curves and surfaces in $$\mathbf R^n$$ enclosing prescribed multi-volume. Zbl 0985.49025
Morgan, Frank
2000
Riemannian geometry. A beginner’s guide. 2nd ed., revised paperback printing. Zbl 1234.53001
Morgan, Frank
2009
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0529.49022
Morgan, Frank
1983
Least-volume representatives of homology classes in $$G(2,C^ 4)$$. Zbl 0679.53060
Morgan, Frank
1989
Colloquium: Soap bubble clusters. Zbl 1205.53009
Morgan, Frank
2007
Generic uniqueness for hypersurfaces minimizing the integral of an elliptic integrand with constant coefficients. Zbl 0423.53042
Morgan, Frank
1981
Cylindrical surfaces of Delaunay. Zbl 1097.53003
Morgan, Frank
2004
Streams of cylindrical water. Zbl 1075.53009
Morgan, Frank
2004
An isoperimetric inequality for the thread problem. Zbl 0893.49029
Morgan, Frank
1997
Survey lectures on geometric measure theory. Zbl 0915.49025
Morgan, Frank
1993
Instability of the wet $$X$$ soap film. Zbl 0965.53012
Brakke, Kenneth; Morgan, Frank
1998
Calibrations and the size of Grassmann faces. Zbl 0766.53048
Morgan, Frank
1992
Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture. Zbl 1355.53005
Morgan, Frank
2016
Strict calibrations, constant mean curvature and triple junctions. Zbl 0867.53008
Morgan, Frank
1995
Soap films and mathematics. Zbl 0804.53009
Morgan, Frank
1993
Optimal city hierarchy: a dynamic programming approach to central place theory. Zbl 1309.91110
Hsu, Wen-Tai; Holmes, Thomas J.; Morgan, Frank
2014
Soap bubbles and soap films. Zbl 0774.53005
Morgan, Frank
1990
The isoperimetric problem with density. Zbl 1386.49061
Morgan, Frank
2017
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. Zbl 1338.49089
Morgan, Frank
2016
Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture. Zbl 1355.53005
Morgan, Frank
2016
Optimal city hierarchy: a dynamic programming approach to central place theory. Zbl 1309.91110
Hsu, Wen-Tai; Holmes, Thomas J.; Morgan, Frank
2014
Existence of isoperimetric regions in $$\mathbb{R}^{n}$$ with density. Zbl 1263.49049
Morgan, Frank; Pratelli, Aldo
2013
Are large perimeter-minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular? Zbl 1371.74233
Cox, S. J.; Morgan, F.; Graner, F.
2013
Isoperimetric pentagonal tilings. Zbl 1253.52009
Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Sordo Vieira, Luis; Wikner, Elena
2012
The log-convex density conjecture. Zbl 1238.49062
Morgan, Frank
2011
Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Zbl 1229.49046
Morgan, Frank; Howe, Sean; Harman, Nate
2011
The Gauss-Bonnet formula on surfaces with densities. Zbl 1251.53002
Corwin, Ivan; Morgan, Frank
2011
Stable constant-mean-curvature hypersurfaces are area minimizing in small $$L^1$$ neighborhoods. Zbl 1195.49055
Morgan, Frank; Ros, Antonio
2010
Baserunner’s optimal path. Zbl 1187.00008
Carozza, Davide; Johnson, Stewart; Morgan, Frank
2010
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 4th ed. Zbl 1179.49050
Morgan, Frank
2009
Manifolds with density and Perelman’s proof of the Poincaré conjecture. Zbl 1170.53001
Morgan, Frank
2009
Isoperimetric comparison theorems for manifolds with density. Zbl 1175.49042
Maurmann, Quinn; Morgan, Frank
2009
Riemannian geometry. A beginner’s guide. 2nd ed., revised paperback printing. Zbl 1234.53001
Morgan, Frank
2009
Isoperimetric balls in cones over tori. Zbl 1171.53040
Morgan, Frank
2009
On the isoperimetric problem in Euclidean space with density. Zbl 1126.49038
Rosales, César; Cañete, Antonio; Bayle, Vincent; Morgan, Frank
2008
The Levy-Gromov isoperimetric inequality in convex manifolds with boundary. Zbl 1149.53021
Morgan, Frank
2008
In polytopes, small balls about some vertex minimize perimeter. Zbl 1132.49036
Morgan, Frank
2007
Rotation in a normed plane. Zbl 1140.51013
Cook, Jack; Lovett, Jonathan; Morgan, Frank
2007
When soap bubbles collide. Zbl 1183.52015
Adams, Colin; Morgan, Frank; Sullivan, John M.
2007
Colloquium: Soap bubble clusters. Zbl 1205.53009
Morgan, Frank
2007
Myer’s theorem with density. Zbl 1132.53306
Morgan, Frank
2006
Isoperimetric estimates in products. Zbl 1097.49027
Morgan, Frank
2006
Manifolds with density. Zbl 1118.53022
Morgan, Frank
2005
Planar Wulff shape is unique equilibrium. Zbl 1071.49025
Morgan, Frank
2005
Clusters with multiplicities in $$\mathbb R^2$$. Zbl 1108.49034
Morgan, Frank
2005
A round ball uniquely minimizes gravitational potential energy. Zbl 1066.70010
Morgan, Frank
2005
Hexagonal surfaces of Kapouleas. Zbl 1117.53010
Morgan, Frank
2005
Geometric measure theory and the proof of the double bubble conjecture. Zbl 1125.49033
Morgan, Frank; Ritoré, Manuel
2005
Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in $$\mathbb R^n$$. Zbl 1085.52501
Morgan, Frank
2005
Cylindrical surfaces of Delaunay. Zbl 1097.53003
Morgan, Frank
2004
Streams of cylindrical water. Zbl 1075.53009
Morgan, Frank
2004
Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Zbl 1063.49031
Morgan, Frank
2003
Proof of the double bubble conjecture. Zbl 1009.53007
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio
2002
Isoperimetric regions in cones. Zbl 0988.53028
Morgan, Frank; Ritoré, Manuel
2002
Hexagonal economic regions solve the location problem. Zbl 1026.90059
Morgan, Frank; Bolton, Roger
2002
An isoperimetric comparison theorem for Schwarzschild space and other manifolds. Zbl 0994.53029
Bray, Hubert; Morgan, Frank
2002
The standard double bubble is the unique stable double bubble in $$\mathbb{R}^2$$. Zbl 1003.53010
Morgan, Frank; Wichiramala, Wacharin
2002
Area-minimizing surfaces in cones. Zbl 1035.58011
Morgan, Frank
2002
Proof of the double bubble conjecture. Zbl 0990.49029
Morgan, Frank
2001
Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020
Morgan, Frank; Johnson, David L.
2000
Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025
Morgan, Frank
2000
The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Zbl 0976.53082
Morgan, Frank; Hutchings, Michael; Howards, Hugh
2000
Proof of the double bubble conjecture. Zbl 0970.53009
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio
2000
Perimeter-minimizing curves and surfaces in $$\mathbf R^n$$ enclosing prescribed multi-volume. Zbl 0985.49025
Morgan, Frank
2000
The isoperimetric problem on surfaces. Zbl 1003.52011
Howards, Hugh; Hutchings, Michael; Morgan, Frank
1999
Isoperimetric curves on hyperbolic surfaces. Zbl 0992.53048
1999
The hexagonal honeycomb conjecture. Zbl 0932.49032
Morgan, Frank
1999
Riemannian geometry. A beginner’s guide. 2nd ed. Zbl 0911.53001
Morgan, Frank
1998
Immiscible fluid clusters in $${\mathbb{R}}^2$$ and $${\mathbb{R}}^3$$. Zbl 0967.49026
Morgan, Frank
1998
Wulff clusters in $$\mathbb{R}^2$$. Zbl 0934.49024
Morgan, Frank; French, Christopher; Greenleaf, Scott
1998
Instability of the wet $$X$$ soap film. Zbl 0965.53012
Brakke, Kenneth; Morgan, Frank
1998
Lower semicontinuity of energy clusters. Zbl 0886.49016
Morgan, Frank
1997
An isoperimetric inequality for the thread problem. Zbl 0893.49029
Morgan, Frank
1997
Open problems in soap bubble geometry. Zbl 0867.53009
Sullivan, John M.; Morgan, Frank
1996
Geodesic nets on the $$2$$-sphere. Zbl 0871.53038
Hass, Joel; Morgan, Frank
1996
Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006
Lawlor, Gary; Morgan, Frank
1996
Geodesics and soap bubbles in surfaces. Zbl 0865.53009
Hass, Joel; Morgan, Frank
1996
Geometric measure theory. A beginner’s guide. 2nd ed. Zbl 0819.49024
Morgan, Frank
1995
Volume-minimizing cycles in Grassmann manifolds. Zbl 0837.53035
Gluck, Herman; Mackenzie, Dana; Morgan, Frank
1995
Strict calibrations, constant mean curvature and triple junctions. Zbl 0867.53008
Morgan, Frank
1995
Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Zbl 0830.49028
Lawlor, Gary; Morgan, Frank
1994
The isoperimetric theorem for general integrands. Zbl 0923.49019
Brothers, John E.; Morgan, Frank
1994
Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002
Morgan, Frank
1994
Clusters minimizing area plus length of singular curves. Zbl 0805.49025
Morgan, Frank
1994
$$(M,\varepsilon,\delta)$$-minimal curve regularity. Zbl 0804.49033
Morgan, Frank
1994
Surfaces minimizing area plus length of singular curves. Zbl 0816.49033
Morgan, Frank
1994
Mathematicians, including undergraduates, look at soap bubbles. Zbl 0814.53002
Morgan, Frank
1994
Riemannian geometry. A beginner’s guide. Zbl 0794.53001
Morgan, Frank
1993
Survey lectures on geometric measure theory. Zbl 0915.49025
Morgan, Frank
1993
Soap films and mathematics. Zbl 0804.53009
Morgan, Frank
1993
Minimal surfaces, crystals, shortest networks, and undergraduate research. Zbl 0765.52015
Morgan, Frank
1992
Calibrations and the size of Grassmann faces. Zbl 0766.53048
Morgan, Frank
1992
The cone over the Clifford torus in $$R^ 4$$ is $$\Phi$$-minimizing. Zbl 0725.49013
Morgan, Frank
1991
Singularities of minimal surfaces and networks and related extremal problems in Minkowski space. Zbl 0762.49014
Füredi, Z.; Lagarias, J. C.; Morgan, F.
1991
Calibrations and new singularities in area-minimizing surfaces: A survey. Zbl 0721.53058
Morgan, Frank
1990
Soap bubbles and soap films. Zbl 0774.53005
Morgan, Frank
1990
A sharp counterexample on the regularity of $$\Phi$$-minimizing hypersurfaces. Zbl 0696.49074
Morgan, Frank
1990
Calibrated geometries in Grassmann manifolds. Zbl 0681.53039
Gluck, Herman; Morgan, Frank; Ziler, Wolfgang
1989
Size-minimizing rectifiable currents. Zbl 0645.49024
Morgan, Frank
1989
Least-volume representatives of homology classes in $$G(2,C^ 4)$$. Zbl 0679.53060
Morgan, Frank
1989
Geometric measure theory. A beginner’s guide. Zbl 0671.49043
Morgan, Frank
1988
Area-minimizing surfaces, faces of Grassmannians, and calibrations. Zbl 0672.49028
Morgan, Frank
1988
Calibrations on $${\mathbb{R}}^ 8$$. Zbl 0666.49015
Dadok, J.; Harvey, R.; Morgan, F.
1988
Calibrations modulo $$\nu$$. Zbl 0618.49019
Morgan, Frank
1987
Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $$\nu$$. Zbl 0617.49019
Morgan, Frank
1986
The faces of the Grassmannian of 3-planes in $${\mathbb{R}}^ 7$$ (calibrated geometries on $${\mathbb{R}}^ 7)$$. Zbl 0556.53036
Harvey, Reese; Morgan, Frank
1986
A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027
Morgan, Frank
1986
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0592.53004
Morgan, Frank
1986
The comass ball in $$\Lambda ^ 3({\mathbb{R}}^ 6)^*$$. Zbl 0594.53045
Harvey, Reese; Morgan, Frank
1986
The exterior algebra $$\Lambda ^ kR^ n$$ and area minimization. Zbl 0585.49029
Morgan, Frank
1985
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0572.49021
Morgan, Frank
1985
Area-minimizing currents bounded by higher multiples of curves. Zbl 0541.49018
Morgan, Frank
1984
Examples of unoriented area-minimizing surfaces. Zbl 0509.53007
Morgan, Frank
1984
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0557.49022
Morgan, Frank
1983
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0529.49022
Morgan, Frank
1983
On the singular structure of two-dimensional area minimizing surfaces in $${\mathbb{R}}^ n$$. Zbl 0549.49029
Morgan, Frank
1982
Measures on spaces of surfaces. Zbl 0529.58031
Morgan, Frank
1982
...and 5 more Documents
all top 5

### Cited by 981 Authors

 52 Morgan, Frank 16 de Lima, Henrique F. 12 Novaga, Matteo 10 Milman, Emanuel 10 Paolini, Emanuele 10 Pratelli, Aldo 10 Swanepoel, Konrad J. 9 Ambrosio, Luigi 9 Chiacchio, Francesco 9 Rosales, César 8 Brock, Friedemann 8 Garcke, Harald 8 López Camino, Rafael 8 Maggi, Francesco 8 Nardulli, Stefano 8 Ritoré, Manuel 7 Mercaldo, Anna 7 Santos, Márcio S. 6 Lawlor, Gary R. 5 Bellettini, Giovanni 5 Brakke, Kenneth A. 5 Bucur, Dorin 5 Cañete, Antonio 5 Figalli, Alessio 5 Fragalà, Ilaria 5 Hieu, Doan The 5 Hutchings, Michael Lounsbery 5 Liang, Xiangyu 5 Posteraro, Maria Rosaria 5 Ros, Antonio 5 Velásquez, Marco Antonio Lázaro 4 Altin, Mustafa 4 Alvino, Angelo 4 Bouchitté, Guy 4 Bueno, Antonio 4 Buttazzo, Giuseppe 4 Caraballo, David G. 4 Dewar, Sean 4 Giga, Yoshikazu 4 Goldman, Michael 4 Hardt, Robert M. 4 Hass, Joel 4 Karadaǧ, Haci Bayram 4 Katz, Mikhail G. 4 Kazan, Ahmet 4 Koiso, Miyuki 4 Lê Hông Vân 4 Li, Haizhong 4 Marchese, Andrea 4 Mondino, Andrea 4 Mucci, Domenico 4 Neumayer, Robin 4 Oliveira, Arlandson Matheus Silva 4 Paolini, Maurizio 4 Pérez Muñoz, Joaquín 4 Petean, Jimmy 4 Ros-Oton, Xavier 4 Ruiz, Juan Miguel 4 Saracco, Giorgio 4 Stepanov, Eugene 4 Tanaka, Minoru 4 Topaloglu, Ihsan 4 Vernadakis, Efstratios 4 White, Brian Cabell 4 Yoon, Dae Won 3 Abels, Helmut 3 Alama, Stan 3 Alberti, Giovanni 3 Antonelli, Gioacchino 3 Arroja Neves, André 3 Batista, Márcio 3 Bérard, Pierre H. 3 Bronsard, Lia 3 Cabré, Xavier 3 Castro, Katherine 3 Chambolle, Antonin 3 Choksi, Rustum 3 Cinti, Eleonora 3 Conti, Sergio 3 Corneli, Joseph 3 Dadok, Jiri 3 de Lima, Eudes Leite 3 De Philippis, Guido 3 Delladio, Silvano 3 Filliman, Paul 3 Fonseca, Irene 3 Fusco, Nicola 3 Garroni, Adriana 3 Giaquinta, Mariano 3 He, Guoqing 3 Heilman, Steven M. 3 Helffer, Bernard 3 Ilias, Saïd 3 Ivanov, Sergei Vladimirovich 3 Kloeckner, Benoît R. 3 Le Nam, Tran 3 Leonardi, Gian Paolo 3 Li, Xingxiao 3 Lin, Fang Hua 3 Liu, Yangyang ...and 881 more Authors
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### Cited in 232 Serials

 49 The Journal of Geometric Analysis 42 Calculus of Variations and Partial Differential Equations 35 Transactions of the American Mathematical Society 30 Proceedings of the American Mathematical Society 22 Archive for Rational Mechanics and Analysis 21 Advances in Mathematics 20 Duke Mathematical Journal 19 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Annals of Global Analysis and Geometry 17 Journal of Mathematical Analysis and Applications 17 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Inventiones Mathematicae 14 Geometriae Dedicata 14 Mathematische Annalen 14 Mathematische Zeitschrift 10 Journal of Differential Equations 10 Journal of Functional Analysis 10 Manuscripta Mathematica 9 Discrete & Computational Geometry 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal für die Reine und Angewandte Mathematik 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Differential Geometry and its Applications 7 Journal of Geometry and Physics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Advances in Calculus of Variations 6 Annales de l’Institut Fourier 6 Revista Matemática Iberoamericana 5 Communications in Mathematical Physics 5 Results in Mathematics 5 Geometric and Functional Analysis. GAFA 5 Experimental Mathematics 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Analysis and Geometry in Metric Spaces 4 Communications on Pure and Applied Mathematics 4 Israel Journal of Mathematics 4 Journal of Computational Physics 4 Kodai Mathematical Journal 4 Memoirs of the American Mathematical Society 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 SIAM Journal on Mathematical Analysis 4 Journal of Mathematical Sciences (New York) 4 Geometry & Topology 4 Communications in Contemporary Mathematics 4 Communications on Pure and Applied Analysis 3 Bulletin of the Australian Mathematical Society 3 The Mathematical Intelligencer 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal of Geometry 3 Mathematika 3 Pacific Journal of Mathematics 3 Acta Applicandae Mathematicae 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Mathematical Imaging and Vision 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Discrete and Continuous Dynamical Systems 3 Interfaces and Free Boundaries 3 Journal of the European Mathematical Society (JEMS) 3 Annales Henri Poincaré 3 Journal of Evolution Equations 3 Foundations of Computational Mathematics 3 Missouri Journal of Mathematical Sciences 2 Discrete Mathematics 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Rocky Mountain Journal of Mathematics 2 Acta Mathematica 2 Archiv der Mathematik 2 Illinois Journal of Mathematics 2 Journal of Differential Geometry 2 Journal of Economic Theory 2 Journal of the Mathematical Society of Japan 2 Networks 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 Tôhoku Mathematical Journal. Second Series 2 European Journal of Combinatorics 2 Advances in Applied Mathematics 2 Ergodic Theory and Dynamical Systems 2 Journal of the American Mathematical Society 2 Annals of Operations Research 2 The Annals of Applied Probability 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Communications in Partial Differential Equations 2 Linear Algebra and its Applications 2 Expositiones Mathematicae 2 Potential Analysis 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 St. Petersburg Mathematical Journal 2 Electronic Research Announcements of the American Mathematical Society 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Conformal Geometry and Dynamics 2 Journal of Inequalities and Applications 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Journal of High Energy Physics ...and 132 more Serials
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### Cited in 51 Fields

 418 Differential geometry (53-XX) 343 Calculus of variations and optimal control; optimization (49-XX) 115 Partial differential equations (35-XX) 105 Global analysis, analysis on manifolds (58-XX) 86 Convex and discrete geometry (52-XX) 55 Measure and integration (28-XX) 35 Functional analysis (46-XX) 34 Geometry (51-XX) 31 Probability theory and stochastic processes (60-XX) 29 Manifolds and cell complexes (57-XX) 26 Operations research, mathematical programming (90-XX) 25 Mechanics of deformable solids (74-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Real functions (26-XX) 22 Numerical analysis (65-XX) 21 Combinatorics (05-XX) 20 Fluid mechanics (76-XX) 17 Dynamical systems and ergodic theory (37-XX) 13 Computer science (68-XX) 12 Potential theory (31-XX) 12 Relativity and gravitational theory (83-XX) 9 Functions of a complex variable (30-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Ordinary differential equations (34-XX) 8 Statistics (62-XX) 8 Quantum theory (81-XX) 7 Algebraic geometry (14-XX) 7 Group theory and generalizations (20-XX) 7 Biology and other natural sciences (92-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Operator theory (47-XX) 6 General topology (54-XX) 6 Algebraic topology (55-XX) 5 Mechanics of particles and systems (70-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Information and communication theory, circuits (94-XX) 4 Topological groups, Lie groups (22-XX) 4 Difference and functional equations (39-XX) 4 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX)

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