Spaces of Lorentzian and real stable polynomials are Euclidean balls

Lorentzian Geodesic Flows between Hypersurfaces in Euclidean Spaces

There are several approaches to this question. One is from the perspective of a Riemannian metric on the group of diffeomorphisms of R. If the smooth hypersurfaces Mi bound compact regions Ωi , then the group of diffeomorphisms Diff(R) acts on such regions Ωi and their boundaries. Then, if φt, 1 ≤ t ≤ 1, is a geodesic in Diff(R) beginning at the identity, then φt(Ω) (or φt(Mi)) provides a path ...

From Euclidean to Lorentzian general relativity: The real way.

We study in this paper a new approach to the problem of relating solutions to the Einstein field equations with Riemannian and Lorentzian signatures. The procedure can be thought of as a “real Wick rotation”. We give a modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations. We show how this proc...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Simplicial Euclidean and Lorentzian Quantum Gravity

One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over Euclidean geometries can be performed constructively by the method of dynamical triangulations. One can define a proper-time propagator. This propagator can be used to calculate generalized Hartle-Hawking amplitudes and it can be used to understand the the fractal structure of quantum ...

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.