The Willmore conjecture for immersed tori with small curvature integral

Authors
Ammann, B
Citation
B. Ammann, The Willmore conjecture for immersed tori with small curvature integral, MANUSC MATH, 101(1), 2000, pp. 1-22
Citations number
20
Categorie Soggetti
Mathematics
Journal title
MANUSCRIPTA MATHEMATICA
ISSN journal
00252611 → ACNP
Volume
101
Issue
1
Year of publication
2000
Pages
1 - 22
Database
ISI
SICI code
0025-2611(200001)101:1<1:TWCFIT>2.0.ZU;2-U
Abstract
The Willmore conjecture states that any immersion F : T-2 --> R-n of a 2-to rus into euclidean space satisfies integral(T2) H-2 greater than or equal t o 2 pi(2). We prove it under the condition that the L-p-norm of the Gaussia n curvature is sufficiently small.