# zbMATH — the first resource for mathematics

## 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: 125 Publications since 1976, including 13 Books
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#### Co-Authors

 82 single-authored 4 Hutchings, Michael Lounsbery 4 Ritoré, Manuel 4 Sullivan, John M. jun. 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 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 1 Dadok, Jiri 1 Fernández, Miguel Ángel 1 French, Christopher P. 1 Furedi, Zoltan 1 Graner, François 1 Greenleaf, Scott 1 Gulliver, Robert D. II 1 Harman, Nate 1 Holmes, Thomas J. 1 Howe, Sean 1 Hsu, Wen-Tai 1 Johnson, David Lewis 1 Johnson, Stewart D. 1 Kern, Norbert 1 Lagarias, Jeffrey C. 1 Larché, Francis 1 Li, Yifei 1 Lovett, Jonathan 1 Mackenzie, Dana Walter Nance 1 Mara, Michael Kelly 1 Maurmann, Quinn 1 Miller, Steven J. 1 Newkirk, Edward 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 Vieira, Luis Sordo 1 Wichiramala, Wacharin 1 Wikner, Elena 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 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 Involve 1 Analysis and Geometry in Metric Spaces 1 MAA Spectrum
all top 5

#### Fields

 86 Calculus of variations and optimal control; optimization (49-XX) 82 Differential geometry (53-XX) 14 Convex and discrete geometry (52-XX) 13 Global analysis, analysis on manifolds (58-XX) 7 Measure and integration (28-XX) 5 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 Relativity and gravitational theory (83-XX) 3 Operations research, mathematical programming (90-XX) 3 Mathematics education (97-XX) 2 History and biography (01-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

102 Publications have been cited 1,260 times in 734 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
Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025
Morgan, Frank
2000
Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Zbl 1063.49031
Morgan, Frank
2003
Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Zbl 0830.49028
Lawlor, Gary; Morgan, Frank
1994
Proof of the double bubble conjecture. Zbl 1009.53007
Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio
2002
Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020
Morgan, Frank; Johnson, David L.
2000
Geometric measure theory. A beginner’s guide. 2nd ed. Zbl 0819.49024
Morgan, Frank
1995
The isoperimetric problem on surfaces. Zbl 1003.52011
Howards, Hugh; Hutchings, Michael; Morgan, Frank
1999
Existence of isoperimetric regions in $$\mathbb{R}^{n}$$ with density. Zbl 1263.49049
Morgan, Frank; Pratelli, Aldo
2013
Isoperimetric regions in cones. Zbl 0988.53028
Morgan, Frank; Ritoré, Manuel
2002
Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002
Morgan, Frank
1994
The isoperimetric theorem for general integrands. Zbl 0923.49019
Brothers, John E.; Morgan, Frank
1994
The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Zbl 0976.53082
Morgan, Frank; Hutchings, Michael; Howards, Hugh
2000
Clusters minimizing area plus length of singular curves. Zbl 0805.49025
Morgan, Frank
1994
Hexagonal economic regions solve the location problem. Zbl 1026.90059
Morgan, Frank; Bolton, Roger
2002
On the singular structure of two-dimensional area minimizing surfaces in $${\mathbb{R}}^ n$$. Zbl 0549.49029
Morgan, Frank
1982
The exterior algebra $$\Lambda ^ kR^ n$$ and area minimization. Zbl 0585.49029
Morgan, Frank
1985
Manifolds with density and Perelman’s proof of the Poincaré conjecture. Zbl 1170.53001
Morgan, Frank
2009
Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. Zbl 1338.49089
Morgan, Frank
2016
Myer’s theorem with density. Zbl 1132.53306
Morgan, Frank
2006
An isoperimetric comparison theorem for Schwarzschild space and other manifolds. Zbl 0994.53029
Bray, Hubert; Morgan, Frank
2002
The cone over the Clifford torus in $$R^ 4$$ is $$\Phi$$-minimizing. Zbl 0725.49013
Morgan, Frank
1991
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0557.49022
Morgan, Frank
1983
Riemannian geometry. A beginner’s guide. 2nd ed. Zbl 0911.53001
Morgan, Frank
1998
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
In polytopes, small balls about some vertex minimize perimeter. Zbl 1132.49036
Morgan, Frank
2007
The log-convex density conjecture. Zbl 1238.49062
Morgan, Frank
2011
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
Open problems in soap bubble geometry. Zbl 0867.53009
Sullivan, John M.; Morgan, Frank
1996
Volume-minimizing cycles in Grassmann manifolds. Zbl 0837.53035
Gluck, Herman; Mackenzie, Dana; Morgan, Frank
1995
Examples of unoriented area-minimizing surfaces. Zbl 0509.53007
Morgan, Frank
1984
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
Riemannian geometry. A beginner’s guide. Zbl 0794.53001
Morgan, Frank
1993
Planar Wulff shape is unique equilibrium. Zbl 1071.49025
Morgan, Frank
2005
Isoperimetric estimates in products. Zbl 1097.49027
Morgan, Frank
2006
Stable constant-mean-curvature hypersurfaces are area minimizing in small $$L^1$$ neighborhoods. Zbl 1195.49055
Morgan, Frank; Ros, Antonio
2010
Calibrated geometries in Grassmann manifolds. Zbl 0681.53039
Gluck, Herman; Morgan, Frank; Ziler, Wolfgang
1989
$$(M,\varepsilon,\delta)$$-minimal curve regularity. Zbl 0804.49033
Morgan, Frank
1994
The standard double bubble is the unique stable double bubble in $$\mathbb{R}^2$$. Zbl 1003.53010
Morgan, Frank; Wichiramala, Wacharin
2002
Immiscible fluid clusters in $${\mathbb{R}}^2$$ and $${\mathbb{R}}^3$$. Zbl 0967.49026
Morgan, Frank
1998
Measures on spaces of surfaces. Zbl 0529.58031
Morgan, Frank
1982
Almost every curve in $$R^3$$ bounds a unique area minimizing surface. Zbl 0378.49028
Morgan, Frank
1978
Lower semicontinuity of energy clusters. Zbl 0886.49016
Morgan, Frank
1997
Calibrations and new singularities in area-minimizing surfaces: A survey. Zbl 0721.53058
Morgan, Frank
1990
Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Zbl 1229.49046
Morgan, Frank; Howe, Sean; Harman, Nate
2011
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
A smooth curve in $$R^4$$ bounding a continuum of area minimizing surfaces. Zbl 0338.53003
Morgan, Frank
1976
Surfaces minimizing area plus length of singular curves. Zbl 0816.49033
Morgan, Frank
1994
Isoperimetric curves on hyperbolic surfaces. Zbl 0992.53048
1999
The hexagonal honeycomb conjecture. Zbl 0932.49032
Morgan, Frank
1999
Wulff clusters in $$\mathbb{R}^2$$. Zbl 0934.49024
Morgan, Frank; French, Christopher; Greenleaf, Scott
1998
Area-minimizing surfaces in cones. Zbl 1035.58011
Morgan, Frank
2002
Geodesic nets on the $$2$$-sphere. Zbl 0871.53038
Hass, Joel; Morgan, Frank
1996
A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027
Morgan, Frank
1986
Size-minimizing rectifiable currents. Zbl 0645.49024
Morgan, Frank
1989
The Levy-Gromov isoperimetric inequality in convex manifolds with boundary. Zbl 1149.53021
Morgan, Frank
2008
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
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
Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006
Lawlor, Gary; Morgan, Frank
1996
Proof of the double bubble conjecture. Zbl 0990.49029
Morgan, Frank
2001
A round ball uniquely minimizes gravitational potential energy. Zbl 1066.70010
Morgan, Frank
2005
Hexagonal surfaces of Kapouleas. Zbl 1117.53010
Morgan, Frank
2005
Calibrations modulo $$\nu$$. Zbl 0618.49019
Morgan, Frank
1987
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
Mathematicians, including undergraduates, look at soap bubbles. Zbl 0814.53002
Morgan, Frank
1994
Perimeter-minimizing curves and surfaces in $$\mathbf R^n$$ enclosing prescribed multi-volume. Zbl 0985.49025
Morgan, Frank
2000
Instability of the wet $$X$$ soap film. Zbl 0965.53012
Brakke, Kenneth; Morgan, Frank
1998
When soap bubbles collide. Zbl 1183.52015
Adams, Colin; Morgan, Frank; Sullivan, John M.
2007
Rotation in a normed plane. Zbl 1140.51013
Cook, Jack; Lovett, Jonathan; Morgan, Frank
2007
Geometric measure theory and the proof of the double bubble conjecture. Zbl 1125.49033
Morgan, Frank; Ritoré, Manuel
2005
Isoperimetric pentagonal tilings. Zbl 1253.52009
Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Vieira, Luis Sordo; Wikner, Elena
2012
On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0529.49022
Morgan, Frank
1983
The Gauss-Bonnet formula on surfaces with densities. Zbl 1251.53002
Corwin, Ivan; Morgan, Frank
2011
Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in $$\mathbb R^n$$. Zbl 1085.52501
Morgan, Frank
2005
Least-volume representatives of homology classes in $$G(2,C^ 4)$$. Zbl 0679.53060
Morgan, Frank
1989
A smooth curve in $$R^ 3$$ bounding a continuum of minimal manifolds. Zbl 0453.49027
Morgan, Frank
1981
The symmetry group of a curve preserves a plane. Zbl 0489.53002
Gulliver, Robert; Morgan, Frank
1982
Riemannian geometry. A beginner’s guide. 2nd ed., revised paperback printing. Zbl 1234.53001
Morgan, Frank
2009
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0572.49021
Morgan, Frank
1985
Survey lectures on geometric measure theory. Zbl 0915.49025
Morgan, Frank
1993
Strict calibrations, constant mean curvature and triple junctions. Zbl 0867.53008
Morgan, Frank
1995
Streams of cylindrical water. Zbl 1075.53009
Morgan, Frank
2004
Cylindrical surfaces of Delaunay. Zbl 1097.53003
Morgan, Frank
2004
Baserunner’s optimal path. Zbl 1187.00008
Carozza, Davide; Johnson, Stewart; Morgan, Frank
2010
Isoperimetric balls in cones over tori. Zbl 1171.53040
Morgan, Frank
2009
A sharp counterexample on the regularity of $$\Phi$$-minimizing hypersurfaces. Zbl 0696.49074
Morgan, Frank
1990
Calibrations and the size of Grassmann faces. Zbl 0766.53048
Morgan, Frank
1992
Soap bubbles and soap films. Zbl 0774.53005
Morgan, Frank
1990
Soap films and mathematics. Zbl 0804.53009
Morgan, Frank
1993
Generic uniqueness for hypersurfaces minimizing the integral of an elliptic integrand with constant coefficients. Zbl 0423.53042
Morgan, Frank
1981
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
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; Vieira, Luis Sordo; 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
When soap bubbles collide. Zbl 1183.52015
Adams, Colin; Morgan, Frank; Sullivan, John M.
2007
Rotation in a normed plane. Zbl 1140.51013
Cook, Jack; Lovett, Jonathan; 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
Streams of cylindrical water. Zbl 1075.53009
Morgan, Frank
2004
Cylindrical surfaces of Delaunay. Zbl 1097.53003
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
Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025
Morgan, Frank
2000
Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020
Morgan, Frank; Johnson, David L.
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
Geodesics and soap bubbles in surfaces. Zbl 0865.53009
Hass, Joel; Morgan, Frank
1996
Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006
Lawlor, Gary; 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
Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002
Morgan, Frank
1994
The isoperimetric theorem for general integrands. Zbl 0923.49019
Brothers, John E.; 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
A sharp counterexample on the regularity of $$\Phi$$-minimizing hypersurfaces. Zbl 0696.49074
Morgan, Frank
1990
Soap bubbles and soap films. Zbl 0774.53005
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
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0592.53004
Morgan, Frank
1986
A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027
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
The symmetry group of a curve preserves a plane. Zbl 0489.53002
Gulliver, Robert; Morgan, Frank
1982
A smooth curve in $$R^ 3$$ bounding a continuum of minimal manifolds. Zbl 0453.49027
Morgan, Frank
1981
Generic uniqueness for hypersurfaces minimizing the integral of an elliptic integrand with constant coefficients. Zbl 0423.53042
Morgan, Frank
1981
...and 2 more Documents
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#### Cited by 906 Authors

 53 Morgan, Frank 12 de Lima, Henrique F. 10 Swanepoel, Konrad J. 9 Chiacchio, Francesco 9 Milman, Emanuel 9 Novaga, Matteo 9 Pratelli, Aldo 8 Ambrosio, Luigi 8 Brock, Friedemann 8 López Camino, Rafael 8 Maggi, Francesco 8 Paolini, Emanuele 8 Rosales, César 7 Garcke, Harald 7 Mercaldo, Anna 7 Ritoré, Manuel 7 Santos, Márcio S. 6 Lawlor, Gary R. 5 Bellettini, Giovanni 5 Brakke, Kenneth A. 5 Figalli, Alessio 5 Fragalà, Ilaria 5 Hieu, Doan The 5 Hutchings, Michael Lounsbery 5 Nardulli, Stefano 5 Posteraro, Maria Rosaria 5 Ros, Antonio 4 Abels, Helmut 4 Altin, Mustafa 4 Alvino, Angelo 4 Bouchitté, Guy 4 Bucur, Dorin 4 Buttazzo, Giuseppe 4 Cañete, Antonio 4 Caraballo, David G. 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 Li, Haizhong 4 Liang, Xiangyu 4 Marchese, Andrea 4 Mondino, Andrea 4 Mucci, Domenico 4 Oliveira, Arlandson Matheus Silva 4 Paolini, Maurizio 4 Pérez Muñoz, Joaquín 4 Petean, Jimmy 4 Ruiz, Juan Miguel 4 Saracco, Giorgio 4 Tanaka, Minoru 4 Velásquez, Marco Antonio Lázaro 4 White, Brian Cabell 4 Yoon, Dae Won 3 Alberti, Giovanni 3 Arroja Neves, André 3 Bueno, Antonio 3 Cabré, Xavier 3 Chambolle, Antonin 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 Ilias, Saïd 3 Ivanov, Sergei Vladimirovich 3 Kloeckner, Benoît R. 3 Koiso, Miyuki 3 Lê Hông Vân 3 Le Nam, Tran 3 Lin, Fang Hua 3 Lytchak, Alexander 3 Marques, Fernando Codá 3 Meeks, William Hamilton III 3 Millot, Vincent 3 Miquel, Vicente 3 Modica, Giuseppe 3 Neumayer, Robin 3 Nicolaescu, Liviu I. 3 Nishimura, Takashi 3 Nürnberg, Robert 3 Palmer, Bennett 3 Pluda, Alessandra 3 Ren, Xiaofeng 3 Rimoldi, Michele 3 Ros-Oton, Xavier 3 Ross, Marty 3 Salavessa, Isabel M. C. 3 Santambrogio, Filippo 3 Shouman, Abdolhakim ...and 806 more Authors
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#### Cited in 216 Serials

 43 The Journal of Geometric Analysis 35 Calculus of Variations and Partial Differential Equations 34 Transactions of the American Mathematical Society 29 Proceedings of the American Mathematical Society 21 Archive for Rational Mechanics and Analysis 21 Advances in Mathematics 18 Duke Mathematical Journal 17 Annals of Global Analysis and Geometry 15 Journal of Mathematical Analysis and Applications 15 Inventiones Mathematicae 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 14 Geometriae Dedicata 14 Mathematische Annalen 14 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Mathematische Zeitschrift 10 Journal of Functional Analysis 10 Manuscripta Mathematica 9 Journal of Differential Equations 9 Discrete & Computational Geometry 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Journal für die Reine und Angewandte Mathematik 7 Journal of Geometry and Physics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Differential Geometry and its Applications 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Annales de l’Institut Fourier 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Advances in Calculus of Variations 5 Revista Matemática Iberoamericana 5 Analysis and Geometry in Metric Spaces 4 Communications in Mathematical Physics 4 Communications on Pure and Applied Mathematics 4 Israel Journal of Mathematics 4 Journal of Computational Physics 4 The Mathematical Intelligencer 4 Kodai Mathematical Journal 4 Results in Mathematics 4 Geometric and Functional Analysis. GAFA 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 SIAM Journal on Mathematical Analysis 4 Experimental Mathematics 4 Journal of Mathematical Sciences (New York) 4 Geometry & Topology 4 Communications in Contemporary Mathematics 4 Communications on Pure and Applied Analysis 4 Bulletin of the Brazilian Mathematical Society. New Series 3 Bulletin of the Australian Mathematical Society 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Mathematika 3 Memoirs of the American Mathematical Society 3 Pacific Journal of Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Mathematical Imaging and Vision 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 Journal of Geometry 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 Advances in Applied Mathematics 2 Acta Applicandae Mathematicae 2 Probability Theory and Related Fields 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 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Potential Analysis 2 St. Petersburg Mathematical Journal 2 Electronic Research Announcements of the American Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Abstract and Applied Analysis 2 Conformal Geometry and Dynamics 2 Analysis (München) 2 Interfaces and Free Boundaries 2 Acta Mathematica Sinica. English Series 2 Advances in Geometry 2 International Journal of Geometric Methods in Modern Physics 2 Mediterranean Journal of Mathematics 2 International Electronic Journal of Geometry 2 Involve 2 Science China. Mathematics 2 Geometric Flows 2 Bollettino dell’Unione Matematica Italiana 1 Applicable Analysis 1 General Relativity and Gravitation ...and 116 more Serials
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#### Cited in 51 Fields

 369 Differential geometry (53-XX) 309 Calculus of variations and optimal control; optimization (49-XX) 105 Partial differential equations (35-XX) 94 Global analysis, analysis on manifolds (58-XX) 77 Convex and discrete geometry (52-XX) 51 Measure and integration (28-XX) 32 Functional analysis (46-XX) 32 Geometry (51-XX) 29 Probability theory and stochastic processes (60-XX) 26 Manifolds and cell complexes (57-XX) 25 Mechanics of deformable solids (74-XX) 22 Operations research, mathematical programming (90-XX) 21 Real functions (26-XX) 21 Numerical analysis (65-XX) 21 Statistical mechanics, structure of matter (82-XX) 18 Fluid mechanics (76-XX) 17 Combinatorics (05-XX) 16 Dynamical systems and ergodic theory (37-XX) 12 Potential theory (31-XX) 12 Computer science (68-XX) 10 Several complex variables and analytic spaces (32-XX) 8 Group theory and generalizations (20-XX) 8 Functions of a complex variable (30-XX) 8 Statistics (62-XX) 8 Relativity and gravitational theory (83-XX) 7 Algebraic geometry (14-XX) 7 Ordinary differential equations (34-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) 5 Algebraic topology (55-XX) 5 Quantum theory (81-XX) 5 Information and communication theory, circuits (94-XX) 4 Topological groups, Lie groups (22-XX) 4 Difference and functional equations (39-XX) 4 Mechanics of particles and systems (70-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Integral transforms, operational calculus (44-XX) 3 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 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) 1 Classical thermodynamics, heat transfer (80-XX)

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