×

Steiner and Schwarz symmetrization in warped products and fiber bundles with density. (English) Zbl 1229.49046

Summary: We provide very general symmetrization theorems in arbitrary dimension and codimension, in products, warped products, and certain fiber bundles such as lens spaces, including Steiner, Schwarz, and spherical symmetrization and admitting density.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
53C12 Foliations (differential geometric aspects)
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] Benjamini, I. and Cao, J.: A new isoperimetric comparison theorem for surfaces of variable curvature. Duke Math. J. 85 (1996), 359-396. · Zbl 0886.53031
[2] Burago, Yu. D. and Zalgaller, V. A.: Geometric inequalities. Die Grundlehren der mathematischen Wissenschaften 285. Springer-Verlag, 1988.
[3] Chavel, I.: Riemannian geometry. A modern introduction. Cambridge Studies in Advanced Mathematics 98. Cambridge University Press, 2006. · Zbl 1099.53001
[4] Chlebí\?k, M., Cianchi, A. and Fusco, N.: The perimeter inequality under Steiner symmetrization: cases of equality. Ann. of Math. (2) 162 (2005), 525-555. · Zbl 1087.28003
[5] Díaz, A., Harman, N., Howe, S. and Thompson, D.: Isoperimetric problems in sectors with density. To appear in Adv. Geom. · Zbl 1263.49061
[6] Federer, H.: Geometric measure theory. Die Grundlehren der mathema- tischen Wissenschaften 153. Springer-Verlag, 1969. · Zbl 0176.00801
[7] Gromov, M.: Isoperimetry of waists and concentration of maps. Geom. Funct. Anal. 13 (2003), 178-215. · Zbl 1044.46057
[8] Gromov, M.: Spectral geometry of semi-algebraic sets. Ann. Inst. Fourier (Grenoble) 42 (1992), 249-274. · Zbl 0759.58048
[9] Monti, R.: Heisenberg isoperimetric problem. The axial case. Adv. Calc. Var. 1 (2008), 93-121. · Zbl 1149.49036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.