| Title: | On the Gromov hyperbolicity of the minimal metric |
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| Authors: | ID Fiacchi, Matteo (Author) |
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| Files: |  PDF - Presentation file, download (330,70 KB)
MD5: 0A5979D64343E4A9971E73184AA294C5
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00209-024-03581-x
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In this paper we study the hyperbolicity in the sense of Gromov of domains in $\mathbb{R}^d$ $(d\geq3)$ with respect to the minimal metric introduced by Forstnerič and Kalaj. In particular, we prove that every bounded strongly minimally convex domain is Gromov hyperbolic and its Gromov compactification is equivalent to its Euclidean closure. Moreover, we prove that the boundary of a Gromov hyperbolic convex domain does not contain non-trivial conformal harmonic disks. Finally, we study the relation between the minimal metric and the Hilbert metric in convex domains. |
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| Keywords: | minimal surfaces, minimal metric, hyperbolic domain, Gromov hyperbolicity, convex domain, Hilbert metric |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.10.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 20 str. |
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| Numbering: | Vol. 308, iss. 2, [article no.] 24 |
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| UDC: | 517.5 |
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| ISSN on article: | 0025-5874 |
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| DOI: | 10.1007/s00209-024-03581-x  |
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| COBISS.SI-ID: | 206119939 |
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| Note: |
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| Publication date in DiRROS: | 05.09.2024 |
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| Views: | 17 |
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| Downloads: | 8 |
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| Metadata: |     |
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