Centro-Affine Invariants for Smooth Convex Bodies

Details Centro-Affine Invariants for Smooth Convex Bodies Centro-Affine Invariants for Smooth Convex Bodies

2010-11-23

arxiv.org/abs/1011.4980v1

Mathematics

Differential Geometry

21 pages

Scientific paper

Employing a centro-affine flow on smooth convex bodies, we generate new centro-affine differential invariants. One class of the newly defined invariants is the object of a sharp isoperimetric inequality, while other new inequalities on known centro-affine invariants are obtained as a byproduct of the flow's study. Furthermore, this approach led to a geometric interpretation of a new affine surface area recently introduced by Ludwig and Reitzner.

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