Abstract
This paper investigates the regularity of constrained Willmore immersions into ℝm≥3 locally around both “regular” points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions for the immersion and its first and second derivatives, given in terms of residues computed as circulation integrals. We deduce explicit “point removability” conditions ensuring that the immersion is smooth. Our results apply in particular to Willmore immersions and to parallel mean curvature immersions in any codimension.
| Original language | English |
|---|---|
| Pages (from-to) | 1513-1552 |
| Number of pages | 40 |
| Journal | Communications in Partial Differential Equations |
| Volume | 41 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2 Oct 2016 |
Keywords
- Conformal Willmore equation
- regularity
- singular behaviour
- singularity removability
- Willmore energy
Cite this
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Analysis of constrained Willmore surfaces. / Bernard, Yann.
In: Communications in Partial Differential Equations, Vol. 41, No. 10, 02.10.2016, p. 1513-1552.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Analysis of constrained Willmore surfaces
AU - Bernard, Yann
PY - 2016/10/2
Y1 - 2016/10/2
N2 - This paper investigates the regularity of constrained Willmore immersions into ℝm≥3 locally around both “regular” points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions for the immersion and its first and second derivatives, given in terms of residues computed as circulation integrals. We deduce explicit “point removability” conditions ensuring that the immersion is smooth. Our results apply in particular to Willmore immersions and to parallel mean curvature immersions in any codimension.
AB - This paper investigates the regularity of constrained Willmore immersions into ℝm≥3 locally around both “regular” points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions for the immersion and its first and second derivatives, given in terms of residues computed as circulation integrals. We deduce explicit “point removability” conditions ensuring that the immersion is smooth. Our results apply in particular to Willmore immersions and to parallel mean curvature immersions in any codimension.
KW - Conformal Willmore equation
KW - regularity
KW - singular behaviour
KW - singularity removability
KW - Willmore energy
UR - http://www.scopus.com/inward/record.url?scp=84991085182&partnerID=8YFLogxK
U2 - 10.1080/03605302.2016.1222543
DO - 10.1080/03605302.2016.1222543
M3 - Article
VL - 41
SP - 1513
EP - 1552
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 10
ER -