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arXiv · 1409.7585

(Weak) $m$-extremals and $m$-geodesics

Tomasz Warszawski
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Abstract

We present a collection of results on (weak) $m$-extremals and $m$-geodesics, concerning general properties, the planar case, quasi-balanced pseudoconvex domains, complex ellipsoids, the Euclidean ball and boundary properties. We prove $3$-geodesity of $3$-extremals in the Euclidean ball. Equivalence of weak $m$-extremality and $m$-extremality in some class of convex complex ellipsoids, containing symmetric ones and $\mathcal C^2$-smooth ones is showed. Moreover, first examples of $3$-extremals being not $3$-geodesics in convex domains are given.

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Tomasz Warszawski. 2014-09-26. (Weak) $m$-extremals and $m$-geodesics. https://doi.org/10.1080/17476933.2014.998659

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