We consider the irrational Aubry-Mather sets of an exact symplectic monotone C 1 twist map, introduce for them a notion of " C 1-regularity " (related to the notion of Bouligand paratingent cone) and prove that : • a Mather measure has zero Lyapunov exponents iff its support is almost everywhere C 1-regular; • a Mather measure has non zero Lyapunov exponents iff its support is almost everywhere...

We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with denoising lower-level constraints. For problem, we able to derive M-stationarity conditions, after characterizing corresponding Mordukhovich generalized normal cone and verifying suitable constraint qualification conditions....

We prove that any analytic set in $\C^n$ with a unique tangent cone at infinity is an algebraic set. the degree of complex $\C^n$, which Lipschitz normally embedded infinity, equal to its infinity.

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense any linear of horizontal tangent realized by a global isometry. will show these have canonical partial connection defined on their bundle. However, unlike Riemannian case, such are not uniquely determined curvature and metric cone. Furthermore, number invariants needed to determine model with same cone ge...

We develop a mathematical framework for describing local features of a geometric object— such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a tangent complex for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic fe...

When rendering objects with hardware tessellation, back-facing patches should be culled as early as possible to avoid unnecessary surface evaluations, and setup costs for the tessellator and rasterizer. For dynamic objects the popular cone-of-normals approach is usually approximated using tangent and bitangent cones. This is faster to compute, but less effective. We present a novel approach usi...

The aim of the article is to study Betti numbers tangent cone Gorenstein monomial curves in affine 4-space. If $C_S$ a noncomplete intersection curve whose Cohen--Macaulay, we show that possible sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).