Isoperimetric inequalities for parametric variational problems

Ulrich Clarenz; Heiko von der Mosel

Annales de l'I.H.P. Analyse non linéaire (2002)

  • Volume: 19, Issue: 5, page 617-629
  • ISSN: 0294-1449

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Clarenz, Ulrich, and von der Mosel, Heiko. "Isoperimetric inequalities for parametric variational problems." Annales de l'I.H.P. Analyse non linéaire 19.5 (2002): 617-629. <http://eudml.org/doc/78556>.

@article{Clarenz2002,
author = {Clarenz, Ulrich, von der Mosel, Heiko},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {minimal surfaces; critical immersions; isoperimetric inequality},
language = {eng},
number = {5},
pages = {617-629},
publisher = {Elsevier},
title = {Isoperimetric inequalities for parametric variational problems},
url = {http://eudml.org/doc/78556},
volume = {19},
year = {2002},
}

TY - JOUR
AU - Clarenz, Ulrich
AU - von der Mosel, Heiko
TI - Isoperimetric inequalities for parametric variational problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 5
SP - 617
EP - 629
LA - eng
KW - minimal surfaces; critical immersions; isoperimetric inequality
UR - http://eudml.org/doc/78556
ER -

References

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  1. [1] Barbosa J.L., do Carmo M., A proof of a general isoperimetric inequality for surfaces, Math. Z.162 (3) (1978) 245-261. Zbl0369.53054MR508841
  2. [2] Beckenbach E.F., Radó T., Subharmonic functions and surfaces of negative curvature, Trans. Am. Math. Soc.35 (1933) 662-664. Zbl0007.13001MR1501708
  3. [3] U. Clarenz, Enclosure theorems for extremals of elliptic parametric functionals, Calc. Var., online publication DOI 10.1007/s005260100128, 2001. Zbl1018.53006MR1938817
  4. [4] Clarenz U., von der Mosel H., Compactness theorems and an isoperimetric inequality for critical points of elliptic parametric functionals, Calc. Var.12 (2001) 85-107. Zbl0968.35039MR1808108
  5. [5] Courant R., Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience, New York, 1950. Zbl0040.34603MR36317
  6. [6] Dierkes U., Hildebrandt S., Küster A., Wohlrab O., Minimal Surfaces, Vol. I, Grundlehren math. Wiss., 295, Springer, Berlin, 1992. Zbl0777.53012
  7. [7] Heinz E., Hildebrandt S., The number of branch points of surfaces of bounded mean curvature, J. Differential Geom.4 (1970) 227-235. Zbl0195.23003MR267495
  8. [8] Hildebrandt S., Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, Math. Z.112 (1969) 205-213. Zbl0175.40403MR250208
  9. [9] Hildebrandt S., von der Mosel H., On two-dimensional variational problems, Calc. Var.9 (1999) 249-267. Zbl0934.49022MR1725204
  10. [10] S. Hildebrandt, H. von der Mosel, Plateau's problem for parametric double integrals: I. Existence and regularity in the interior, Preprint 88 MPI f. Math. Leipzig, 2001. Preprint 745 SFB 256 Univ. Bonn, 2001, to appear in Comm. Pure. Appl. Math. Zbl1031.49038MR1990482
  11. [11] Sauvigny F., Introduction of isothermal parameters into a Riemannian metric by the continuity method, Analysis19 (1999) 235-243. Zbl0936.35046MR1715172

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