Optimal isosystolic inequalities on real projective planes

Optimal isosystolic inequalities on real projective planes

Unai Lejarza Alonso – GJM, Volume 8, Issue 2 (2023), 46-72.

In this article all known optimal isosystolic inequalities on real projective planes are stated and proved. First the well-known proof for the Riemannian case is reproduced in a slightly more modern style. Then the Finslerian cases for both the Holmes-Thompson and the Busemann-Hausdorff areas are treated. Following Ivanov [10], a slight generalisation of the theorem for reversible Finslerian metrics and the Holmes-Thompson area is proved. Using the Blaschke-Santaló inequality, the theorem for reversible Finslerian metrics and the Busemann-Hausdorff area follows easily. Finally, systolic freedom is proved for non reversible Finslerian metrics and the Busemann-Hausdorff area.

Categories: Issue2

Milestones:

Received: June 26, 2023
Accepted: December 21, 2023
Revised: December 30, 2023

Authors:

Unai Lejarza Alonso
Universitat Autònoma de Barcelona,
Plaça Cívica, 08193 Bellaterra, Barcelona, Spain.

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