Recent study has shown that a non-singular oscillating potential – a feature of Infinite Derivative Gravity (IDG) theories – matches current experimental data better than the standard GR potential. In this work we show that this non-singular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays, and therefore geodesic completeness. We consolida...

Donaldson conjectured[14] that the space of Kähler metrics is geodesic convex by smooth geodesic and that it is a metric space. Following Donaldson’s program, we verify the second part of Donaldson’s conjecture completely and verify his first part partially. We also prove that the constant scalar curvature metric is unique in each Kähler class if the first Chern class is either strictly negativ...

We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is λ-geodesically convex for some λ ∈ R. Also, we prove a general stability result for gradient flows of geodesically convex functionals which Γ−converge to some limit functional. The stability result applies directly to the case of the Entropy functionals on compact sp...

A 3rd order numerical model is developed for global advection transport computation. The multi-moment finite volume method has been implemented to the hexagonal-pentagonal geodesic grid for spherical geometry. Two kinds of moments, i.e. point value and volume-integrated average, are used as the constraint conditions to derive the time evolution equations to update the computational variables, w...

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong linear properties. This negative result hints that radial kernel are perhaps not suitable over geo...

Local primitives and their spatial relationships are useful in the analysis, recognition and retrieval of document and patent binary images. In this paper, a morphology based approach is proposed to establish the connections between the local primitives found at the optimally detected junction points and end points. The grayscale geodesic dilation is employed as the basic technique by taking a ...

*Correspondence: Valter Moretti, Dipartimento di Matematica, Università di Trento and Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento, via Sommarive 14 I-38050 Povo, Italy e-mail: [email protected] A spacetime is locally flat if and only if no geodesical deviation exists for congruences of all kinds of geodesics. However, while for causal geodesics the deviation can be m...

In this paper, we study the problem of constructing a family of surfaces from a given spatial geodesic curve. We derive a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve. By utilizing the Frenet trihedron frame along the given geodesic, we express the surface pencil as a linear combination of the components of this local coord...

In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems of equations. One system of equations is solved repeatedly to propagate the wave on the entire mesh, and one system is solved once after wave propagation is c...

We present a heuristic algorithm to compute approximate geodesic distances on a triangular manifold S containing n vertices with partially missing data. The proposed method computes an approximation of the geodesic distance between two vertices pi and pj on S and provides an upper bound of the geodesic distance that is shown to be optimal in the worst case. This yields a relative error bound of...