[Sur le problème isopérimétrique de Berger]
Berger’s isoperimetric problem asks if the flat equilateral torus is
Le problème isopérimétrique de Berger demande si le tore plat équilatéral est
Révisé le :
Accepté le :
Publié le :
Fan Kang 1

@article{CRMATH_2025__363_G7_695_0, author = {Fan Kang}, title = {On {Berger{\textquoteright}s} isoperimetric problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {695--704}, publisher = {Acad\'emie des sciences, Paris}, volume = {363}, year = {2025}, doi = {10.5802/crmath.749}, language = {en}, }
Fan Kang. On Berger’s isoperimetric problem. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 695-704. doi : 10.5802/crmath.749. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.749/
[1] Seminar on differential geometry (Shing-Tung Yau, ed.), Annals of Mathematics Studies, 102, Princeton University Press, 1982, ix+706 pages | DOI | MR | Zbl
[2] Sur les premières valeurs propres des variétés riemanniennes, Compos. Math., Volume 26 (1973) no. 2, pp. 129-149 | DOI | Numdam | MR | Zbl
[3] On the conformal volume of 2-tori (2015) | arXiv | Zbl
[4] On branched minimal immersions of surfaces by first eigenfunctions, Ann. Global Anal. Geom., Volume 56 (2019) no. 4, pp. 667-690 | DOI | MR | Zbl
[5] A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle, Duke Math. J., Volume 135 (2006) no. 1, pp. 181-202 | DOI | MR | Zbl
[6] Immersions minimales, première valeur propre du laplacien et volume conforme, Math. Ann., Volume 275 (1986), pp. 257-267 | DOI | MR | Zbl
[7] Extremal metrics for the first eigenvalue of the Laplacian in a conformal class, Proc. Am. Math. Soc., Volume 131 (2003) no. 5, pp. 1611-1618 | DOI | Zbl
[8] Sur la première valeur propre des tores, Sémin. Théor. Spectr. Géom., Volume 15 (1996), pp. 17-23 | DOI | Numdam | Zbl
[9] Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Math., Volume 270 (1970), p. A1645-A1648 | Zbl
[10] How large can the first eigenvalue be on a surface of genus two?, Int. Math. Res. Not., Volume 2005 (2005) no. 63, pp. 3967-3985 | DOI | MR | Zbl
[11] Extremal metric for the first eigenvalue on a Klein bottle, Can. J. Math., Volume 58 (2006) no. 2, pp. 381-400 | DOI | MR | Zbl
[12] A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math., Volume 69 (1982) no. 2, pp. 269-291 | DOI | MR | Zbl
[13] Minimal immersions of surfaces by the first eigenfunctions and conformal area, Invent. Math., Volume 83 (1986), pp. 153-166 | DOI | MR | Zbl
[14] Berger’s isoperimetric problem and minimal immersions of surfaces, Geom. Funct. Anal., Volume 6 (1996) no. 5, pp. 877-897 | DOI | MR | Zbl
[15] Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian, C. R. Math., Volume 357 (2019) no. 1, pp. 84-98 | DOI | Numdam | Zbl
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