2005 LMS Whitehead Prize

Dr Bernd Kirchheim of the University of Oxford was awarded a Whitehead Prize for his fundamental work in several areas of real analysis. His results in geometric measure theory include a proof that rectifiable metric spaces have density one, a metric differentiation theorem, and a surprisingly powerful extension with Ambrosio of the Federer-Fleming theory of currents to general metric spaces. His results in the calculus of variations include a proof that the quasiconvex envelope of a continuously differentiable function remains continuously differentiable and a complete solution to the problem of existence of non-trivial Lipschitz self-maps of the plane whose gradients attain only finitely many values.