A gap theorem for Willmore tori and an application to the Willmore flow

Mondino, Andrea and Nguyen, Huy The (2014) A gap theorem for Willmore tori and an application to the Willmore flow. Nonlinear Analysis: Theory, Methods and Applications, 102 220-225. doi:10.1016/j.na.2014.02.015


Author Mondino, Andrea
Nguyen, Huy The
Title A gap theorem for Willmore tori and an application to the Willmore flow
Journal name Nonlinear Analysis: Theory, Methods and Applications   Check publisher's open access policy
ISSN 0362-546X
1873-5215
Publication date 2014-06
Year available 2014
Sub-type Article (original research)
DOI 10.1016/j.na.2014.02.015
Open Access Status
Volume 102
Start page 220
End page 225
Total pages 6
Place of publication Oxford, United Kingdom
Publisher Pergamon Press
Collection year 2015
Language eng
Formatted abstract
In 1965, Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2 and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves (2012). In this paper, we show for tori that there is a gap to the next critical point of the Willmore energy and we discuss an application to the Willmore flow. We also prove an energy gap from the Clifford torus to surfaces of higher genus.
Keyword Geometric analysis
Willmore functional
Surface theory
Nonlinear elliptic equation of 4th order
Geometric flows
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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