mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, Lawson's

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

states that the

Clifford torus In geometric topology, the Clifford torus is the simplest and most symmetric flat embedding of the Cartesian product of two circles and (in the same sense that the surface of a cylinder is "flat"). It is named after William Kingdon Cliffo ...

is the only minimally embedded

torus In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses inclu ...

in the

3-sphere In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere, ''n''-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior o ...

''S''³. The conjecture was featured by the Australian Mathematical Society Gazette as part of the ''Millennium Problems'' series. In March 2012,

Simon Brendle Simon Brendle (born June 1981) is a German-American mathematician working in differential geometry and nonlinear partial differential equations. At the age of 19, he received his Dr. rer. nat. from Tübingen University under the supervision of Ge ...

gave a proof of this conjecture, based on maximum principle techniques.

References

Geometric topology Theorems in differential geometry Conjectures that have been proved Theorems in topology {{topology-stub