Final Report Summary - ISOINEQINTGEO (Isoperimetric Inequalities and Integral Geometry)
The project achievments helped to transform and enhance our understanding of the interplay between the theory of affine isoperimetric inequalities and the theory of valuations.
The underlying bigger picture behind their strong relations has become much clearer over the course of the last five years. A systematic exploitation of the
"valuations point of view", in particular, new algebraic structures on translation invariant valuations, was not only the key to establishing new isosperimetric inequalities but also provided the means to attack long standing major open problems in the area of affine isoperimetric inequalities. Many classical inequalities from affine geometry were shown to hold in a much more general setting than was previously understood and the full strength of affine inequalities compared to
their counterparts from Euclidean geometry was revealed.
The underlying bigger picture behind their strong relations has become much clearer over the course of the last five years. A systematic exploitation of the
"valuations point of view", in particular, new algebraic structures on translation invariant valuations, was not only the key to establishing new isosperimetric inequalities but also provided the means to attack long standing major open problems in the area of affine isoperimetric inequalities. Many classical inequalities from affine geometry were shown to hold in a much more general setting than was previously understood and the full strength of affine inequalities compared to
their counterparts from Euclidean geometry was revealed.