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

• Опубліковано в: Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2022
• ISSN: 1815-0659
• Автор: Tashiro, Kenshiro
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2022
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/211729
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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...