Academic Journal
Finite time singularities of the Kähler–Ricci flow.
| Τίτλος: | Finite time singularities of the Kähler–Ricci flow. |
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| Συγγραφείς: | Jian, Wangjian1 (AUTHOR) wangjian@amss.ac.cn, Song, Jian2 (AUTHOR) jiansong@math.rutgers.edu, Tian, Gang3 (AUTHOR) gtian@math.pku.edu.cn |
| Πηγή: | Inventiones Mathematicae. Sep2026, p1-102. 102p. |
| Θεματικοί όροι: | *Ricci flow, *Mathematical singularities, *Mathematical bounds |
| Περίληψη: | We establish the scalar curvature and distance bounds, extending Perelman’s work on the Fano Kähler–Ricci flow to general finite time solutions of the Kähler–Ricci flow. These bounds are achieved by our Li–Yau type and Harnack estimates for weighted Ricci potential functions of the Kähler–Ricci flow. We further prove that the Type I blow-ups of the finite time solution always sub-converge in Gromov–Hausdorff sense to an ancient solution on a family of analytic normal varieties with suitable choices of base points. As a consequence, the Type I diameter bound is obtained for a fibre over every relatively compact open subset of the regular base of the fibration. We also apply our estimates to show that every solution of the Kähler–Ricci flow with Calabi symmetry must develop Type I singularities, including both cases of high codimensional contractions and fibre collapsing. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s00222-026-01449-x Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Items | – Name: Title Label: Title Group: Ti Data: Finite time singularities of the Kähler–Ricci flow. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jian%2C+Wangjian%22">Jian, Wangjian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wangjian@amss.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Song%2C+Jian%22">Song, Jian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jiansong@math.rutgers.edu</i><br /><searchLink fieldCode="AR" term="%22Tian%2C+Gang%22">Tian, Gang</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> gtian@math.pku.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Inventiones+Mathematicae%22">Inventiones Mathematicae</searchLink>. Sep2026, p1-102. 102p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Ricci+flow%22">Ricci flow</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We establish the scalar curvature and distance bounds, extending Perelman’s work on the Fano Kähler–Ricci flow to general finite time solutions of the Kähler–Ricci flow. These bounds are achieved by our Li–Yau type and Harnack estimates for weighted Ricci potential functions of the Kähler–Ricci flow. We further prove that the Type I blow-ups of the finite time solution always sub-converge in Gromov–Hausdorff sense to an ancient solution on a family of analytic normal varieties with suitable choices of base points. As a consequence, the Type I diameter bound is obtained for a fibre over every relatively compact open subset of the regular base of the fibration. We also apply our estimates to show that every solution of the Kähler–Ricci flow with Calabi symmetry must develop Type I singularities, including both cases of high codimensional contractions and fibre collapsing. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196990538 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00222-026-01449-x Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 102 StartPage: 1 Subjects: – SubjectFull: Ricci flow Type: general – SubjectFull: Mathematical singularities Type: general – SubjectFull: Mathematical bounds Type: general Titles: – TitleFull: Finite time singularities of the Kähler–Ricci flow. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jian, Wangjian – PersonEntity: Name: NameFull: Song, Jian – PersonEntity: Name: NameFull: Tian, Gang IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00209910 Titles: – TitleFull: Inventiones Mathematicae Type: main |
| ResultId | 1 |