Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume
In this paper, we give a systolic inequality for a quotient space of a Carnot group Γ∖ with Popp's volume. Namely, we show the existence of a positive constant C such that the systole of Γ∖ is less than Cvol(Γ∖)¹ᐟQ, where Q is the Hausdorff dimension. Moreover, the constant depends only on the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211729 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume. Kenshiro Tashiro. SIGMA 18 (2022), 058, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862666362232504320 |
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| author | Tashiro, Kenshiro |
| author_facet | Tashiro, Kenshiro |
| citation_txt | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume. Kenshiro Tashiro. SIGMA 18 (2022), 058, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we give a systolic inequality for a quotient space of a Carnot group Γ∖ with Popp's volume. Namely, we show the existence of a positive constant C such that the systole of Γ∖ is less than Cvol(Γ∖)¹ᐟQ, where Q is the Hausdorff dimension. Moreover, the constant depends only on the dimension of the grading of the Lie algebra = ⨁ ᵢ. To prove this fact, the scalar product on introduced in the definition of Popp's volume plays a key role.
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| first_indexed | 2026-03-16T09:46:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211729 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T09:46:39Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
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| spelling | Tashiro, Kenshiro 2026-01-09T12:53:47Z 2022 Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume. Kenshiro Tashiro. SIGMA 18 (2022), 058, 16 pages 1815-0659 2020 Mathematics Subject Classification: 53C17; 26B15; 22E25 arXiv:2201.00128 https://nasplib.isofts.kiev.ua/handle/123456789/211729 https://doi.org/10.3842/SIGMA.2022.058 In this paper, we give a systolic inequality for a quotient space of a Carnot group Γ∖ with Popp's volume. Namely, we show the existence of a positive constant C such that the systole of Γ∖ is less than Cvol(Γ∖)¹ᐟQ, where Q is the Hausdorff dimension. Moreover, the constant depends only on the dimension of the grading of the Lie algebra = ⨁ ᵢ. To prove this fact, the scalar product on introduced in the definition of Popp's volume plays a key role. The author would appreciate to thank Professor Takumi Yokota for many insightful suggestions. The author thanks the referees for many helpful comments on earlier drafts of the manuscript. This research is supported by JSPS KAKENHI grant numbers 18K03298 and 20J13261. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume Article published earlier |
| spellingShingle | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume Tashiro, Kenshiro |
| title | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume |
| title_full | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume |
| title_fullStr | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume |
| title_full_unstemmed | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume |
| title_short | Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume |
| title_sort | systolic inequalities for compact quotients of carnot groups with popp's volume |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211729 |
| work_keys_str_mv | AT tashirokenshiro systolicinequalitiesforcompactquotientsofcarnotgroupswithpoppsvolume |