In: Mathematische Zeitschrift, 2007, vol. 257, no. 1, p. 7-12
We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type.
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In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374
Sinc-interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. It, however, requires that the interpolated function decreases rapidly or is periodic. We give an error formula for the case where neither of these conditions is satisfied.
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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...
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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...
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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.
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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...
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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...
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In: Differential Geometry and its Applications, 2006, vol. 24, no. 6, p. 660-669
We refine recent existence and uniqueness results, for the barycenter of points at infinity of Hadamard manifolds, to measures on the sphere at infinity of symmetric spaces of non compact type and, more specifically, to measures concentrated on single orbits. The barycenter will be interpreted as the maximum likelihood estimate (MLE) of generalized Cauchy distributions on Furstenberg boundaries....
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In: Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, no. 1, p. 233-238
It has been shown by Reed that random-sampling a Wiener process x(t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P(x(T))~x(T)-β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time...
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Thèse de doctorat : Université de Fribourg, 2006 ; Nr. 1522.
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