Abstract
When \(p>0\), the dual \(L_p\) John ellipsoids provide a unified treatment for the Löwner ellipsoid and the Legendre ellipsoid associated with a convex body. When \(p<0\), very little relevance to known ellipsoids has been found for the dual \(L_p\) John ellipsoid so far. In this paper we investigate a sharp dual \(L_p\) John ellipsoid problem associated with origin-symmetric convex bodies when \(p\le -n-1\). The solution unifies the classic John ellipsoid and the classic Petty ellipsoid.
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Lv, S. A sharp dual \(L_{p}\) John ellipsoid problem for \(p\le -n-1\). Beitr Algebra Geom 60, 709–732 (2019). https://doi.org/10.1007/s13366-019-00444-z
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DOI: https://doi.org/10.1007/s13366-019-00444-z