Affiner les résultats

Collection spécifique

Langue

Université de Fribourg

Further remarks on mixed fractional Brownian motion

Thäle, Christoph

In: Applied Mathematical Sciences, 2009, vol. 38, p. 1885-1901

We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension of the sample paths of such processes. Moreover we compare different notions of fractional differentiability and calculate as a second new result explicitly the Cesáro fractional derivative of the...

Université de Fribourg

Hilbert geometry of polytopes

Bernig, Andreas

In: Archiv der Mathematik, 2009, vol. 92, no. 4, p. 314-324

It is shown that the Hilbert metric on the interior of a convex polytope is bilipschitz to a normed vector space of the same dimension.

Université de Fribourg

Polyhedral hyperbolic metrics on surfaces

Fillastre, François

In: Geometriae Dedicata, 2008, vol. 134, no. 1, p. 177-196

Let S be a topologically finite surface, and g be a hyperbolic metric on S with a finite number of conical singularities of positive singular curvature, cusps and complete ends of infinite area. We prove that there exists a convex polyhedral surface P in hyperbolic space ℍ³ and a group G of isometries of ℍ³ such that the induced metric on the quotient P/G is isometric to g. Moreover,...

Université de Fribourg

Valuations on manifolds and Rumin cohomology

Bernig, Andreas ; Bröcker, Ludwig

In: Journal of Differential Geometry, 2007, vol. 75, no. 3, p. 433-457

Smooth valuations on manifolds are studied by establishing a link with the Rumin-de Rham complex of the co-sphere bundle. Several operations on differential forms induce operations on smooth valuations: signature operator, Rumin-Laplace operator, Euler-Verdier involution and derivation operator. As an application, Alesker’s Hard Lefschetz Theorem for even translation invariant valuations on...

Université de Fribourg

Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces

Bernig, Andreas ; Lytchak, Alexander

In: Journal für die reine und angewandte Mathematik, 2007, no. 608, p. 1-15

It is shown that the Gromov-Hausdorff limit of a subanalytic 1-parameter family of compact connected sets (endowed with the inner metric) exists. If the family is semialgebraic, then the limit space can be identified with a semialgebraic set over some real closed field. Different notions of tangent cones (pointed Gromov-Hausdorff limits, blow-ups and Alexandrov cones) for a closed connected...

Université de Fribourg

The normal cycle of a compact definable set

Bernig, Andreas

In: Israel Journal of Mathematics, 2007, vol. 159, no. 1, p. 373-411

An elementary construction of the normal cycle of a compact definable set in Euclidean space (and more generally of a compactly supported constructible function) is given. Here “definable” means definable in some o-minimal structure. The construction is based on the notion of support function and uses only basic o-minimal geometry.

Université de Fribourg

Valuations with Crofton formula and Finsler geometry

Bernig, Andreas

In: Advances in Mathematics, 2007, vol. 210, no. 2, p. 733-753

Valuations admitting a smooth Crofton formula are studied using Geometric Measure Theory and Rumin's cohomology of contact manifolds. The main technical result is a current representation of a valuation with a smooth Crofton formula. A geometric interpretation of Alesker's product is given for such valuations. As a first application in Finsler geometry, a short proof of the theorem of...

Université de Fribourg

Convolution of convex valuations

Bernig, Andreas ; Fu, Joseph H. G.

In: Geometriae Dedicata, 2006, vol. 123, no. 1, p. 153-169

We show that the natural “convolution” on the space of smooth, even, translation- invariant convex valuations on a euclidean space V, obtained by intertwining the product and the duality transform of S. Alesker J. Differential Geom. 63: 63–95, 2003; Geom.Funct. Anal. 14:1–26, 2004 may be expressed in terms of Minkowski sum. Furthermore the resulting product extends naturally to odd...

Université de Fribourg

'Spindles' in symmetric spaces

Quast, Peter

In: Journal of the Mathematical Society of Japan, 2006, vol. 58, no. 4, p. 985-994

We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. If the s-orbit is symmetric such submanifolds are the most important examples of adapted submanifolds, i.e. of submanifolds of symmetric spaces with curvature invariant tangent and normal spaces.

Université de Fribourg

Almost extrinsically homogeneous submanifolds of Euclidean space

Quast, Peter

In: Annals of Global Analysis and Geometry, 2006, vol. 29, no. 1, p. 1-16

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M× Rm = T M⊗ ν M is equipped with an almost metric connection ~ ∇ which almost preserves the decomposition of M× Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂~∇ with the usual...