2021/04/23 by Ortega-Moreno, Oscar, Schuster, Franz E. · 1 citation
#52A39 #52A40 #52B45 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2104.11552
It is shown that for any sufficiently regular even Minkowski valuation Φ which is homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where balls are the only solutions to the fixed-point problem Φ2 K = αK. This significantly generalizes results by Ivaki for projection bodies and suggests, via the Lutwak--Schneider class reduction technique, a new approach to Petty's conjectured projection inequality.