Related papers: Invariant Hulls and Geometric Variational Principl…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

Bands of vector-valued functions $f:T\mapsto\mathbb{R}^d$ are defined by considering convex hulls generated by their values concatenated at $m$ different values of the argument. The obtained $m$-bands are families of functions, ranging from…

Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

The objet of this paper is the study of the variations of a functional whose integrant is the r-th weighted curvature on the hypersurface of a closed Riemannian manifold. Some applications to hypersurfaces of the Euclidean space and the…

Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…

We revisit the notion of parametrization invariance while introducing certain weakened notions of invariance in the calculus of variations. In this work, we employ a straightforward approach in the classical setting and mostly restrict…

Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$

We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of…

This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in…

Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…

Covariance functions are a fundamental tool for modeling the dependence structure of spatial processes. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in…

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…

We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…

In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time…

Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…

Two geodesically (projectively) equivalent Finsler metrics determine a set of invariant volume forms on the projective sphere bundle. Their proportionality factors are geodesically invariant functions and hence they are first integrals.…

We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…