Survey on optimal isosystolic inequalities on the real projective plane

Autors/ores

Paraules clau:

real projective plane, systole, isosystolic inequality, Riemannian metric, Finsler metric, Busemann–Hausdorff area, Holmes–Thompson area.

Resum

Es revisen totes les desigualtats isosistòliques òptimes conegudes al pla projectiu real RP2, comparant-les amb el cas del 2-tor T2. Primer s’introdueixen nocions bàsiques de mètriques de Finsler. Després s’enuncien totes les desigualtats isosistòliques conegudes pel cas reversible i se’n dona la idea de prova. Finalment es tracten les desigualtats òptimes pel cas no-reversible. Actualment es coneixen totes les desigualtats òptimes per T2, tot i que no és així per RP2. S’hi presenten alguns petits progressos i arguments a favor de la desigualtat conjecturada en el cas encara obert.

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Descàrregues

Com citar

Lejarza Alonso, U. (2024). Survey on optimal isosystolic inequalities on the real projective plane. Reports@SCM, 9(1), 21–30. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154338

Número

Vol. 9 Núm. 1 (2024)

Secció

Articles

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