(Weak) $m$-extremals and $m$-geodesics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866929441839513600 |
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| author | Warszawski, Tomasz |
| author_facet | Warszawski, Tomasz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1409_7585 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | (Weak) $m$-extremals and $m$-geodesics Warszawski, Tomasz Complex Variables 32F45, 32E30, 30E05, 93B50, 32A07, 30J10 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. |
| title | (Weak) $m$-extremals and $m$-geodesics |
| topic | Complex Variables 32F45, 32E30, 30E05, 93B50, 32A07, 30J10 |
| url | https://arxiv.org/abs/1409.7585 |