We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with -type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoisin...

We revisit certain path-lifting and path-continuation properties of abstract maps as described in the work F. Browder R. Rheindboldt 1950s 1960s, apply their elegant theory to exponential maps. obtain thereby a number novel results existence multiplicity geodesics joining any two points connected affine manifold, well causal connecting causally related on Lorentzian manifold. These include gene...

We say that Γ has uniform exponential growth if Ent Γ > 0. In [11], remarque 5.12, M. Gromov raised the question whether exponential growth always implies uniform exponential growth. The answer is negative, indeed, in [14] J.S. Wilson gave examples of finitely generated groups of exponential growth and non uniform exponential growth. Nevertheless, exponential growth implies uniform exponential ...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdierential set is established.

We address an interesting question raised by Dos Santos Ferreira, Kenig and Salo [11] about regions Rg ⊂ C for which there can be uniform L 2n n+2 → L 2n n−2 resolvent estimates for ∆g + ζ, ζ ∈ Rg , where ∆g is the Laplace-Beltrami operator with metric g on a given compact boundaryless Riemannian manifold of dimension n ≥ 3. This is related to earlier work of Kenig, Ruiz and the third author [1...

Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension m1 +m2 − 1 in the product X := X1 1 ×X m2 2 of two Hadamard manifolds Xi i of dimension mi with negative curvature bounded away from zero. Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity o...

A logic network to produce the sequency ordered Hadamard matrix H based on the property of gray code and orthogonal group codes is developed. The network uses a counter to generate Rademacher function such that the output of H will be in sequency. A general purpose shift register with output logic is used to establish a sequence of period P corresponding to a given value of order m of the Hadam...