-Capacity and -Hyperbolicity of Submanifolds.
-energy of a curve on LIP-manifolds and on general metric spaces.
Packing dimensions, transversal mappings and geodesic flows.
Pairings, duality, amenability and bounded cohomology
We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.
Paley-Wiener Type Theorems on Harmonic Extensions of H-Type Groups.
Para--Lie groups.
Parabeln mit gemeinsamen isotropem Krümmungskreis.
Parabolic equations with rough data
We survey recent work on local well-posedness results for parabolic equations and systems with rough initial data. The design of the function spaces is guided by tools and constructions from harmonic analysis, like maximal functions, square functions and Carleson measures. We construct solutions under virtually optimal scale invariant conditions on the initial data. Applications include BMO initial data for the harmonic map heat flow and the Ricci-DeTurck flow for initial metrics with small local...
Parabolic geometries as conformal infinities of Einstein metrics
Parabolic geometries determined by filtrations of the tangent bundle
Summary: Let be a real semisimple -graded Lie algebra such that the Lie algebra cohomology group is contained in negative homogeneous degrees. We show that if we choose and denote by the parabolic subgroup determined by the grading, there is an equivalence between regular, normal parabolic geometries of type and filtrations of the tangent bundle, such that each symbol algebra is isomorphic to the graded Lie algebra . Examples of parabolic geometries determined by filtrations of the...
Parabolic isometries of CAT(0) spaces and CAT(0) dimensions.
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product
In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
Paracomplex projective models and harmonic maps into them.
Parallel and nonparallel -structures on Euclidean spaces
Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds
In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces...
Parallel and totally geodesic hypersurfaces of solvable Lie groups
In this paper we consider special examples of homogeneous spaces of arbitrary odd dimension which are given in [5] and [16]. We obtain the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces in both Riemannian and Lorentzian cases.
Parallel displacement of vectors on rheonomous anholonomic manifold
Parallel hypersurfaces
We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
Parallel immersions into spaces of constant curvature and conformal transformations.
Parallel Kaehler Submanifolds of Hermitian Symmetric Spaces.