Strong density results in trace spaces of maps between manifolds

The homological singularities of maps in trace spaces between manifolds

We deal with mappings defined between Riemannian manifolds that belong to a trace space of Sobolev functions. The homological singularities of any such map are represented by a current defined in terms of the boundary of its graph. Under suitable topological assumptions on the domain and target manifolds, we show that the non triviality of the singular current is the only obstruction to the str...

On sequences of maps with finite energies in trace spaces between manifolds

We deal with mappings defined between Riemannian manifolds that belong to trace spaces of Sobolev functions. Such mappings are equipped with a natural energy, equivalent to the fractional norm. We study the class of Cartesian currents that arise as weak limits of sequences of mappings with equibounded energies. Under suitable topological assumptions on the domain and target manifolds, we prove ...

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Investigation of Physical Factors Affecting the Wayfinding of Educational Spaces Children aged 7-12 years old in Rasht, North of Iran

Background Wayfinding involves behavior in order to navigate between the two points of origin and destination. The importance of this issue is considerable; because facility of wayfinding is directly related to improving the efficiency of space, and its psychological effects on human life. This study focuses on the effective physical factors in the wayfinding of ...