Explicit parametrizations of Willmore surfaces

2014 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
E. Atanassov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Willmore Surfaces

scholarly journals On time-like Willmore surfaces in Minkowski space

2011 ◽  
Vol 61 (10) ◽  
pp. 1985-1995 ◽  
Author(s):  
Matthias Bergner ◽  
Lars Schäfer
Keyword(s):  
Minkowski Space ◽  
Willmore Surfaces

scholarly journals Minimal Bubbling for Willmore Surfaces

2020 ◽  
Author(s):  
Nicolas Marque
Keyword(s):  
Willmore Surface ◽  
Willmore Surfaces ◽  
Willmore Energy

Abstract In this paper, we build an explicit example of a minimal bubble on a Willmore surface, showing there cannot be compactness for Willmore immersions of Willmore energy above $16 \pi $. Additionally, we prove an inequality on the 2nd residue for limits of sequences of Willmore immersions with simple minimal bubbles. Doing so, we exclude some gluing configurations and prove compactness for immersed Willmore tori of energy below $12 \pi $.

scholarly journals Reflection of Willmore Surfaces with Free Boundaries

2020 ◽  
pp. 1-18
Author(s):  
Ernst Kuwert ◽  
Tobias Lamm
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Critical Points ◽  
Free Boundaries ◽  
Willmore Functional ◽  
Boundary Constraints ◽  
Free Boundary Conditions ◽  
Immersed Surfaces ◽  
Willmore Surfaces

Abstract We study immersed surfaces in ${\mathbb R}^3$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

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