|Location:||MSRI: Baker Board Room|
Classical Brunn-Minkowski inequality states that n-th root of volume is a concave function with respect to Minkowski addition. Brunn- Minkowski type inequalities have also been proved for other homogeneous functionals; Newtonian capacity, torsional rigidity, etc.. In the first part of my talk, I will discuss this inequality for capacities associated to a nonlinear elliptic PDE.
Classical Minkowski problem asks for finding a convex body with prescribed Gaussian curvature. In the second part of my talk, I will talk about existence and uniqueness problem for a Minkowski problem corresponding to a capacitary function associated to the same elliptic PDE.