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In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms.

J., Takens, F. Palis (1985)

Inventiones mathematicae

Cylindrical contact homology of subcritical Stein-fillable contact manifolds.

Yau, Mei-Lin (2004)

Geometry & Topology

Decomposition of smooth functions of two multidimensional variables

Martin Čadek, Jaromír Šimša (1991)

Czechoslovak Mathematical Journal

Definition und grundlegende Eigenschaften des nichtlinearen adjungierten Operators

Věra Burýšková (1978)

Časopis pro pěstování matematiky

Déformations isomonodromiques des singularités régulières

B. Malgrange (1983)

Recherche Coopérative sur Programme n°25

Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg

Hubert Pesce (1992)

Annales scientifiques de l'École Normale Supérieure

Deformations which preserve the non-immersive locus of a map-germ.

David Mond (1990)

Mathematica Scandinavica

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

Jules, Florence, Lassonde, Marc (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz...

Densité des feuilles de certaines équations de Pfaff à 2 variables

Dominique Cerveau (1983)

Annales de l'institut Fourier

On donne une condition suffisante explicite et générique pour qu’une forme de Pfaff à deux variables complexes ait ses feuilles denses tant localement que globalement.

Density and stability of Morse functions on a stratified space

Roberto Pignoni (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ℓ$ simply connected manifolds when $s \geq 1$

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen (2013)

Confluentes Mathematici

Given a compact manifold $N^{n} \subset ℝ^{ν}$ and real numbers $s \geq 1$ and $1 \leq p < \infty$ , we prove that the class $C^{\infty} ({\bar{Q}}^{m}; N^{n})$ of smooth maps on the cube with values into $N^{n}$ is strongly dense in the fractional Sobolev space $W^{s, p} (Q^{m}; N^{n})$ when $N^{n}$ is $⌊ s p ⌋$ simply connected. For $s p$ integer, we prove weak sequential density of $C^{\infty} ({\bar{Q}}^{m}; N^{n})$ when $N^{n}$ is $s p - 1$ simply connected. The proofs are based on the existence of a retraction of $ℝ^{ν}$ onto $N^{n}$ except for a small subset of $N^{n}$ and on a pointwise estimate of fractional derivatives of composition of maps in $W^{s, p} \cap W^{1, s p}$ .

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Corrigendum and addenda to the paper “Convenient vector spaces embed...”

CR mappings and their holomorphic extension

Critical sets of 2-dimensional compact manifolds.

Critical values lie on a line.

Curves and surfaces in hyperbolic space