Centro-Affine Invariants for Smooth Convex Bodies

By Alina Stancu. 2010

78 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/b3a05fb9fab4073d78463e6e07c4e24423f51d24

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

Cone-volume measure of general centered convex bodies (2016, unknown): “Stancu [42], G.”
A unified flow approach to smooth, even Lp-Minkowski problems (2016, background): “The following theorem was proved in [37] regarding the case p = −n− 1, φ ≡ 1 (in this case the flow belongs to a family of centro-affine normal flows introduced by Stancu in [60]).”
Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[9,12,21,23,26–30,32,35–37,44,46–48,51]).”
The logarithmic Minkowski problem (2012, unknown): “In recent years, cone-volume measures have appeared in e.g. [4], [19], [37], [38], [50], [51], [54], and [59].”
The L-Minkowski problem for −n < p < 1 (2017, background): “Note that κ0(u) = κ(u)/hK(u) is the so called centro-affine curvature (see Ludwig [56] or Stancu [79]), which is equi-affine invariant in the following sense.”
Cone-volume measures of polytopes (2013, unknown): “, [2, 4, 5, 9, 16, 17, 20, 21, 22, 28].”