التفاصيل البيبلوغرافية
| العنوان: |
Minimal area of Finsler disks with minimizing geodesics. |
| المؤلفون: |
Cossarini, Marcos1 marcos.cossarini@u-pec.fr, Sabourau, Stéphane1 stephane.sabourau@u-pec.fr |
| المصدر: |
Journal of the European Mathematical Society (EMS Publishing). 2024, Vol. 26 Issue 3, p985-1029. 45p. |
| مصطلحات موضوعية: |
*INTEGRAL geometry, *DISCRETE geometry, *LOGICAL prediction, *MATHEMATICAL models, *MATHEMATICAL analysis |
| مستخلص: |
We show that the Holmes-Thompson area of every Finsler disk of radius r whose interior geodesics are length-minimizing is at least .... Furthermore, we construct examples showing that the inequality is sharp and observe that equality is attained by a non-rotationally-symmetric metric. This contrasts with Berger's conjecture in the Riemannian case, which asserts that the round hemisphere is extremal. To prove our theorem we discretize the Finsler metric using random geodesics. As an auxiliary result, we include a proof of the integral geometry formulas of Blaschke and Santaló for Finsler manifolds with almost no trapped geodesics. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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