On Montel theorem for mappings with inverse moduli inequalities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916029793304576 |
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| author | Mateljevic, Miodrag Sevost'yanov, Evgeny |
| author_facet | Mateljevic, Miodrag Sevost'yanov, Evgeny |
| contents | This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish that a family of open discrete mappings with the inverse Poletskii inequality, omitting at least one point, is equicontinuous if the majorant responsible for the distortion of the modulus of families of paths under the mapping is integrable over almost all concentric spheres centered at the given point. Since analytic functions with finite multiplicity satisfy the inverse Poletskii inequality, this result generalizes the well-known Montel theorem on the normality of families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13755 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Montel theorem for mappings with inverse moduli inequalities Mateljevic, Miodrag Sevost'yanov, Evgeny Complex Variables 30C65, 31A15, 31B25 This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish that a family of open discrete mappings with the inverse Poletskii inequality, omitting at least one point, is equicontinuous if the majorant responsible for the distortion of the modulus of families of paths under the mapping is integrable over almost all concentric spheres centered at the given point. Since analytic functions with finite multiplicity satisfy the inverse Poletskii inequality, this result generalizes the well-known Montel theorem on the normality of families. |
| title | On Montel theorem for mappings with inverse moduli inequalities |
| topic | Complex Variables 30C65, 31A15, 31B25 |
| url | https://arxiv.org/abs/2602.13755 |