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1
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Resolvent Flows for Convex Functionals and p-Harmonic Maps

100%
Kuwae K.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces.
2
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Curvatures of the diagonal lift from an affine manifold to the linear frame bundle

100%
Kowalski O., Sekizawa M.
Open Mathematics
|
2012
|
tom 10
|
nr 3
837-843
EN
We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.
3
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On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

100%
Calvaruso G., Kowalski O.
Open Mathematics
|
2009
|
tom 7
|
nr 1
124-139
EN
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
4
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On the characteristic connection of gwistor space

84%
Albuquerque R.
Open Mathematics
|
2013
|
tom 11
|
nr 1
149-160
EN
We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.
5
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Harmonicity of vector fields on four-dimensional generalized symmetric spaces

84%
Calvaruso G.
Open Mathematics
|
2012
|
tom 10
|
nr 2
411-425
EN
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.
6
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Dirac and Plateau billiards in domains with corners

69%
Gromov M.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1109-1156
EN
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.
7
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Plateau-Stein manifolds

69%
Gromov M.
Open Mathematics
|
2014
|
tom 12
|
nr 7
923-951
EN
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.
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