On the Normal Gauss map of a tight smooth surface in R3
THEORIE DES ENSEMBLES
NOMBRES REELS
GEOMETRIE DIFFERENTIELLE
SURFACES
KUIPER
HAAB
M/91/34
IHES
06/1991
A4
5 f.
EN
TEXTE
PREPUBLICATION
M_91_34.pdf
1991
There is no Tight continuous immersion of the Klein bottle into R3
THEORIE DES ENSEMBLES
NOMBRES REELS
SURFACES
The imbedding radius ?f and the roation number ? of an immersion of a Cech-circle into R2 are used to prove taht there is no tight immersion f of the Klein bottle into R3
KUIPER
M/83/71
IHES
11/1983
A4
8 f.
EN
TEXTE
PREPUBLICATION
M_83_71.pdf
1983
Polynomial equations for tight surfaces
EQUATIONS POLYNOMIALES
SURFACES
MATHEMATIQUES
KUIPER
M/82/56
IHES
09/1982
A4
6 f.
EN
TEXTE
PREPUBLICATION
M_82_56.pdf
1982
Stable surfaces in euclidean three space : Dedicated to Prof. W. Fenchel in Copenhagen
GEOMETRIE EUCLIDIENNE
SURFACES
STABILITE
This paper consists of two related parts. In A we present smooth maps of the real projective plane P with the non euclidean metric ?, into euclidean spaces such that we can read various interesting properties from the image. We mention and indicate some proofs of known facts. This part is expository. In B we consider C?-stable (in the sense of R. Thom) maps of surfaces in E3. We call these "stable surfaces" for short. The Gauss curvature as a measure (? K d?) then exists although the scalar Gauss curvature K may explode at the C?-stable singularities. The infimum of the total absolute curvature (2?)–1 ? |K d?| of a compact surface M equals 4 – ?(M). This infimum can be reached for any surface in the class of stable maps, but not for all surfaces in the class of immersions, as we know. Stable surfaces of minimal total absolute curvature (tight) are given for the exceptions: the projective plane with 0 or 1 handles and the Klein-bottle. Recall that tight (closed) surfaces in EN are also characterized as those that are divided into at most two (connected) parts by any (hyper-)plane.
KUIPER
M/74/14
IHES
12/1974
A4
21 f.
EN
TEXTE
PREPUBLICATION
M_74_14.pdf
1974
On the Statistical mechanics of surfaces
MECANIQUE STATISTIQUE
PHYSIQUE
SURFACES
MODELE D'ISING
FROHLICH
PFISTER
SPENCER
P/82/20
IHES
1982
A4
17 f.
EN
TEXTE
PREPUBLICATION
P_82_20.pdf
1982