Minimal surfaces based on the catenoid

DAVID HOFFMAN is Professor of Mathematics and Co-Director of the Geometry, Analysis, Numerics and Graphics Center (GANG) at the University of Massachusetts, Amherst. He earned his Ph.D. in mathematics at Stanford, after receiving undergraduate degrees at the University of Rochester (in history and mathematics). He has pursued research and/or teaching at the Universities of Durham and Warwick (UK), Michigan and Stanford, as well as IMPA (Rio de Janeiro, Brazil) and the University of Paris VII. He is the 1990 recipient of the MAA Chauvenet Prize.

[1]  W. Meeks,et al.  Minimal surfaces bounded by convex curves in parallel planes , 1991 .

[2]  R. Schoen Uniqueness, symmetry, and embeddedness of minimal surfaces , 1983 .

[3]  Brian White,et al.  Some recent developments in differential geometry , 1989 .

[4]  Bruce Solomon,et al.  The structure of complete embedded surfaces with constant mean curvature , 1989 .

[5]  David M. Anderson,et al.  Periodic Surfaces of Prescribed Mean Curvature , 1987 .

[6]  W. Meeks,et al.  Embedded minimal surfaces with an infinite number of ends , 1989 .

[7]  H. Karcher Embedded minimal surfaces derived from Scherk's examples , 1988 .

[8]  M. Shiffman ON SURFACES OF STATIONARY AREA BOUNDED BY TWO CIRCLES, OR CONVEX CURVES, IN PARALLEL PLANES* , 1956 .

[9]  Johannes C. C. Nitsche,et al.  On new results in the theory of minimal surfaces , 1965 .

[10]  J. Rubinstein,et al.  Applications of minimax to minimal surfaces and the topology of 3-manifolds , 1987 .

[11]  A. Tromba,et al.  The index theorem for classical minimal surfaces , 1981 .

[12]  A. Schoen Infinite periodic minimal surfaces without self-intersections , 1970 .

[13]  W. Meeks,et al.  Embedded minimal surfaces of finite topology , 2015, Journal für die reine und angewandte Mathematik (Crelles Journal).

[14]  W. Fischer,et al.  On 3-periodic minimal surfaces with non-cubic symmetry , 1988 .

[15]  Michael T. Anderson Curvature estimates for minimal surfaces in $3$-manifolds , 1985 .

[16]  R. Osserman A survey of minimal surfaces , 1969 .

[17]  Richard Schoen,et al.  The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature , 1980 .

[18]  The global theory of doubly periodic minimal surfaces , 1989 .

[19]  H. Karcher The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions , 1989 .

[20]  L. Scriven,et al.  Equilibrium bicontinuous structure , 1976, Nature.

[21]  C. Costa Example of a complete minimal immersion in IR3 of genus one and three-embedded ends , 1984 .

[22]  Brian White New applications of mapping degrees to minimal surface theory , 1989 .

[23]  W. Meeks,et al.  A complete embedded minimal surface in ${\bf R}\sp 3$ with genus one and three ends , 1985 .

[24]  Richard Courant,et al.  Soap Film Experiments with Minimal Surfaces , 1940 .

[25]  S. Smale,et al.  An Infinite Dimensional Version of Sard's Theorem , 1965 .

[26]  Robert B. Kusner,et al.  Conformal geometry and complete minimal surfaces , 1987 .

[27]  S. Hildebrandt The calculus of variations today , 1989 .

[28]  H. Schwarz Gesammelte mathematische Abhandlungen , 1970 .

[29]  D. Hoffman,et al.  A VARIATIONAL APPROACH TO THE EXISTENCE OF COMPLETE EMBEDDED MINIMAL-SURFACES , 1988 .

[30]  A. Tromba,et al.  Extreme curves bound embedded minimal surfaces of the type of the disc , 1978 .

[31]  J. Hadamard,et al.  Les surfaces a courbures opposees et leurs lignes geodesique , 1898 .

[32]  Michael J. Callahan,et al.  Computer graphics tools for the study of minimal surfaces , 1988, CACM.

[33]  David M. Anderson,et al.  Periodic area-minimizing surfaces in block copolymers , 1988, Nature.

[34]  Charles Vernon Boys,et al.  Soap-bubbles, their colours and the forces which mould them , 1912 .

[35]  Charles Hermite,et al.  Oeuvres mathématiques de Riemann , 1898 .

[36]  Stefan Hildebrandt,et al.  Mathematics and optimal form , 1985 .

[37]  On the Boundary Behavior of Minimal Surfaces. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[38]  H. Lawson Lectures On Minimal Submanifolds , 1980 .