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Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant

Gwénaël Massuyeau (2012)

Bulletin de la Société Mathématique de France

Let Σ be a compact connected oriented surface with one boundary component, and let π be the fundamental group of Σ . The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of Σ , whose k -th term consists of the self-homeomorphisms of Σ that act trivially at the level of the k -th nilpotent quotient of π . Morita defined a homomorphism from the k -th term of the Johnson filtration to the third homology group of the k -th nilpotent quotient of π . In this paper, we replace groups...

Instability of the eikonal equation and shape from shading

Ian Barnes, Kewei Zhang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in 2 . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...

Integral formulae for a Riemannian manifold with two orthogonal distributions

Vladimir Rovenski (2011)

Open Mathematics

We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components of the...

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