Piecewise Polynomial Spaces and Geometric Continuity of Curves.
Pierre and Sylvestre: some recollections
Pierrot's theorem for singular Riemannian foliations.
Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.
Pincement de la première valeur propre du laplacien pour les hypersurfaces et rigidité
Robert C. Reilly a obtenu des majorations de la première valeur propre du laplacien pour les hypersurfaces de l’espace euclidien. De plus, il a montré que le cas d’égalité dans ces majorations est atteint uniquement pour les sphères géodésiques. Dans cet exposé, nous nous intéressons au problème de pincement pour ces majorations. Nous montrons que si le cas d’égalité est presque atteint, alors l’hypersurface est proche d’une sphère, en un sens que nous préciserons. Nous déduisons ensuite des résultats...
Pincement des variétés à courbure négative d'après M. Gromov et W. Thurston
Pincement sur le spectre et le volume en courbure de Ricci positive
Pinching constants for hyperbolic manifolds.
Pinching Implies Strong Pinching
Pinching Theorem for the First Eigenvalue on Positively Curved Manifolds.
Pinching Theorem for the First Eigenvalue on Positively Curved Four Manifolds.
Pinwheels and bypasses.
Planar Geodesic Immersions in Pseudo-Euclidean Space.
Planar normal sections on the natural embedding of a real flag manifold.
Planar vector field versions of Carathéodory's and Loewner's conjectures.
Let r = 3, 4, ... , ∞, ω. The Cr-Carathéodory's Conjecture states that every Cr convex embedding of a 2-sphere into R3 must have at least two umbilics. The Cr-Loewner's conjecture (stronger than the one of Carathéodory) states that there are no umbilics of index bigger than one. We show that these two conjectures are equivalent to others about planar vector fields. For instance, if r ≠ ω, Cr-Carathéodory's Conjecture is equivalent to the following one:Let ρ > 0 and β: U ⊂ R2 → R, be of class...
Planes with analogues to Euclidean angular bisectors.
Plateau's problem for H-convex curves.
Plateau's Problem for surfaces of constant mean curvature form a global point of view.
Plateau's Problem for Surfaces of Prescribed Mean Curvature in Given Regions.
Plateau-Stein manifolds
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Platonic triangles of groups.