Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2022
• 1. Verfasser: Tashiro, Kenshiro
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2022
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211729
• 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

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...