In mathematics, the Ehrenpreis conjecture of

Leon Ehrenpreis Eliezer 'Leon' Ehrenpreis (May 22, 1930 – August 16, 2010, Brooklyn) was a mathematician at Temple University who proved the Malgrange–Ehrenpreis theorem, the fundamental theorem about differential operators with constant coefficients. He pre ...

states that for any ''K'' greater than 1, any two closed

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ve ...

s of

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial n ...

at least 2 have finite-degree covers which are ''K''-

quasiconformal In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let ''f'' : ''D' ...

: that is, the covers are arbitrarily close in the Teichmüller metric. A proof was announced by Jeremy Kahn and

Vladimir Markovic Vladimir Marković is a Professor of Mathematics at University of Oxford. He was previously the John D. MacArthur Professor at the California Institute of Technology (2013–2020) and Sadleirian Professor of Pure Mathematics at the University o ...

in January 2011, using their proof of the Surface subgroup conjecture and a newly developed "good

pants Trousers (British English), slacks, or pants are an item of clothing worn from the waist to anywhere between the knees and the ankles, covering both legs separately (rather than with cloth extending across both legs as in robes, skirts, and ...

homology" theory. In June 2012, Kahn and Markovic were given the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

s for their work on these two problems by the

Clay Mathematics Institute The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's sc ...

at a ceremony at

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

References

* 3-manifolds Conjectures that have been proved Theorems in topology {{topology-stub

See also

References