H-surface index formula

Ruben Jakob

Annales de l'I.H.P. Analyse non linéaire (2005)

  • Volume: 22, Issue: 5, page 557-578
  • ISSN: 0294-1449

How to cite

top

Jakob, Ruben. "H-surface index formula." Annales de l'I.H.P. Analyse non linéaire 22.5 (2005): 557-578. <http://eudml.org/doc/78669>.

@article{Jakob2005,
author = {Jakob, Ruben},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {H-surface; index of a fixed point; Čech cohomology},
language = {eng},
number = {5},
pages = {557-578},
publisher = {Elsevier},
title = {H-surface index formula},
url = {http://eudml.org/doc/78669},
volume = {22},
year = {2005},
}

TY - JOUR
AU - Jakob, Ruben
TI - H-surface index formula
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 5
SP - 557
EP - 578
LA - eng
KW - H-surface; index of a fixed point; Čech cohomology
UR - http://eudml.org/doc/78669
ER -

References

top
  1. [1] Böhme R., Tromba A.J., The index theorem for classical minimal surfaces, Ann. of Math.113 (2) (1981) 447-499. Zbl0482.58010MR621012
  2. [2] Courant R., Critical points and unstable minimal surfaces, Proc. N.A.S.27 (1941) 51-57. Zbl67.0368.02MR3484JFM67.0368.02
  3. [3] Courant R., On the first variation of the Dirichlet–Douglas integral and on the method of gradients, Proc. N.A.S.27 (1941) 242-248. Zbl0063.00983MR4741
  4. [4] Dold A., Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology4 (1965) 1-8. Zbl0135.23101MR193634
  5. [5] Dold A., Lectures on Algebraic Topology, Grundlehren Math. Wiss., vol. 200, Springer-Verlag, 1980. Zbl0434.55001MR606196
  6. [6] Eilenberg S., Steenrod N., Foundations of Algebraic Topology, Princeton University Press, 1952. Zbl0047.41402MR50886
  7. [7] Heinz E., On surfaces of constant mean curvature with polygonal boundaries, Arch. Rational Mech. Anal.36 (1970) 335-347. Zbl0191.12002MR279697
  8. [8] Heinz E., An inequality of isoperimetric type for surfaces of constant mean curvature, Arch. Rational Mech. Anal.33 (1970) 155-168. Zbl0176.51602MR238188
  9. [9] Heinz E., Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung, Math. Ann.127 (1954) 258-287. Zbl0055.15303MR70013
  10. [10] Heinz E., Ein Regularitätssatz für Flächen beschränkter mittlerer Krümmung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II.12 (1969) 107-118. Zbl0192.58302MR270313
  11. [11] Hildebrandt S., Über Flächen konstanter mittlerer Krümmung, Math. Z.112 (1969) 107-144. Zbl0183.39501MR250206
  12. [12] Hildebrandt S., Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, Math. Z.112 (1969) 205-213. Zbl0175.40403MR250208
  13. [13] Hildebrandt S., Analysis 2, Springer, 2003. 
  14. [14] C. Imbusch, Eine Anwendung des Mountain-Pass-Lemmas auf den Fragenkreis des Plateauschen Problems und eine Alternative zur Drei-Punkte-Bedingung, Diplomarbeit, Bonn, 1997. Zbl0893.58016MR1616539
  15. [15] Jakob R., Instabile Extremalen des Shiffman-Funktionals, Bonner Math. Schriften362 (2003). Zbl1083.49027MR2069486
  16. [16] R. Jakob, Unstable extremal surfaces of the “Shiffman-functional”, Calc. Var., in press. Zbl1083.49026
  17. [17] Jakob R., H-Flächen-Index-Formel, Bonner Math. Schriften366 (2004). Zbl1087.53009MR2208441
  18. [18] Stöcker R., Zieschang H., Algebraische Topologie 2. Auflage, Teubner, 1994. MR1328835
  19. [19] Struwe M., On a critical point theory for minimal surfaces spanning a wire in R 3 , J. Reine Angew. Math.349 (1984) 1-23. Zbl0521.49028MR743962
  20. [20] Struwe M., Plateau's Problem and the Calculus of Variations, Princeton University Press, 1988. Zbl0694.49028MR992402
  21. [21] Tromba A.J., Degree theory on oriented infinite dimensional varieties and the Morse number of minimal surfaces spanning a curve in R n , Part I: ( n 4 ) , Trans. Amer. Math. Soc.290 (1) (1985) 385-413. Zbl0604.58008MR787972
  22. [22] Tromba A.J., Degree theory on oriented infinite dimensional varieties and the Morse number of minimal surfaces spanning a curve in R 3 , Part II: ( n = 3 ) , Manuscripta Math.48 (1984) 139-161. Zbl0622.58006MR753728

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.