Resources / preprint
Steiner Minimal Trees in the Gromov--Hausdorff Space and in Gromov--Hausdorff Clouds 8VDXGR4SVD
| URI | m2://res/8VDXGR4SVD |
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| Kind | preprint |
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| Creators | I. N. Mikhailov |
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| Date | 2026-10-12 |
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| MSC | 51-XX, 52-XX |
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| Subjects | arxiv math.MG |
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| Scope | in |
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Expressions
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|
| Compact profile space, the Arzel\`a--Ascoli theorem \mycite{Sections 3.5--3.7}{TuzhilinLectures | statement | lemma 5.1 | arxiv |
| 2EPDMGR7X8 | statement | theorem 1.2 | arxiv |
| Cloud | definition | definition 6.1 | arxiv |
| 53FRF72K7K | statement | theorem 1.1 | arxiv |
| Simultaneous tree gluing | statement | corollary 4.2 | arxiv |
| Compact Hausdorff hyperspace, \mycite{Sections 3--4}{TuzhilinLectures | statement | lemma 2.5 | arxiv |
| Fixed-tree minimum | statement | proposition 5.5 | arxiv |
| Finite paths remain in one cloud | statement | lemma 6.2 | arxiv |
| Basic distance facts, \mycite{Chapter 7}{BBI | statement | lemma 2.3 | arxiv |
| Gluing one new space | statement | lemma 4.1 | arxiv |
| Correspondences pass to pointed ultralimits | statement | lemma 6.8 | arxiv |
| Network, length, Steiner vertex | definition | definition 3.1 | arxiv |
| Profiles of a glued tree | statement | lemma 5.2 | arxiv |
| EFBECSA0BP | definition | definition 6.3 | arxiv |
| Minimum on a fixed tree | statement | proposition 6.11 | arxiv |
| Compact replacement | statement | theorem 5.4 | arxiv |
| Bounded, totally bounded, compact | definition | definition 2.1 | arxiv |
| Reduction to tree shapes, \mycite{Chapter 1}{HRW}, \mycite{Chapter 1}{IvanovTuzhilinBook | statement | lemma 3.2 | arxiv |
| Terminal identification | statement | theorem 6.9 | arxiv |
| N8RYJDBKNR | definition | definition 2.2 | arxiv |
| Ambient and correspondence definitions, \mycite{Chapter 7}{BBI | statement | lemma 2.4 | arxiv |
| Zero distance for compact spaces, \mycite{Chapter 7}{BBI | statement | lemma 2.6 | arxiv |
| Compact Steiner minimal trees | statement | theorem 5.6 | arxiv |
| Steiner minimal tree in one cloud | statement | theorem 6.12 | arxiv |
| A tree inside $\cM$ | statement | corollary 5.7 | arxiv |
| Existence in the classical setting, \mycite{Chapter 1}{HRW}, \mycite{Chapter 1}{IvanovTuzhilinNetworks | statement | theorem 3.3 | arxiv |
| Nonprincipal ultrafilter | definition | definition 6.6 | arxiv |
| Isometric coboundedness | definition | definition 6.4 | arxiv |
| Pointed ultralimit | definition | definition 6.7 | arxiv |
| Y0N67KDC19 | example | example 6.5 | arxiv |
| Finite metric spaces in the Gromov--Hausdorff space, \mycite{Theorem 2.1}{INT | statement | theorem 3.4 | arxiv |
Catalogue records
- arxiv: 2610.17400 (work)
- arxiv_text: 2610.17400 (work)
- zbmath_search: 903209925 (work)
