TY - JOUR
T1 - Higher order variations of constant mean curvature surfaces
AU - Koiso, Miyuki
AU - Palmer, Bennett
N1 - Funding Information:
Acknowledgements The first author is supported in part by JSPS KAKENHI Grant Numbers JP25287012, JP26520205, and JP26610016. The second author wishes to acknowledge support by JSPS KAKENHI Grant Number JP26610016 and a travel grant supplied by the College of Science and Engineering of Idaho State University.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - We study the third and fourth variation of area for a compact domain in a constant mean curvature surface when there is a Killing field on R3 whose normal component vanishes on the boundary. Examples are given to show that, in the presence of a zero eigenvalue, the non negativity of the second variation has no implications for the local area minimization of the surface.
AB - We study the third and fourth variation of area for a compact domain in a constant mean curvature surface when there is a Killing field on R3 whose normal component vanishes on the boundary. Examples are given to show that, in the presence of a zero eigenvalue, the non negativity of the second variation has no implications for the local area minimization of the surface.
UR - http://www.scopus.com/inward/record.url?scp=85031424838&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85031424838&partnerID=8YFLogxK
U2 - 10.1007/s00526-017-1246-1
DO - 10.1007/s00526-017-1246-1
M3 - Article
AN - SCOPUS:85031424838
SN - 0944-2669
VL - 56
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 6
M1 - 159
ER -