Related papers: Geometric differentiability of Riemann's non-diffe…

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…

As an application of the Bochner formula, we prove that if a $2$-dimensional Riemannian manifold admits a non-trivial smooth tangent vector field $X$ then its Gauss curvature is the divergence of a tangent vector field, constructed from…

In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…

The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…

Modern formulation of Finsler geometry of a manifold M utilizes the equivalence between this geometry and the Riemannian geometry of VTM, the vertical bundle over the tangent bundle of M, treating TM as the base space. We argue that this…

In this paper we prove that any Riemannian surface, with no restriction of curvature at all, can be decomposed into blocks belonging just to some of these types: generalized Y-pieces, generalized funnels and halfplanes.

In this work, we show that a class of metric-affine gravities can be reduced to a Riemann-Cartan one. The reduction is based on the cancelation of the nonmetricity against the symmetric components of the spin connection. A heuristic proof,…

We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…

We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded…

We prove the Riemann Hypothesis via an analytically regulated surface integral over the critical strip of the Riemann zeta function. The key idea is that the convergence of this normalized integral is equivalent to the condition that all…

This article proves the Riemann hypothesis, which states that all non-trivial zeros of the zeta function have a real part equal to 1/2. We inspect in detail the integral form of the (symmetrized) completed zeta function, which is a product…

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…

We investigate the differentiability properties of real-valued quasiconvex functions f defined on a separable Banach space X. Continuity is only assumed to hold at the points of a dense subset. If so, this subset is automatically residual.…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…

In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

The aim of this paper is to study foliations that remain invariant by parallel transports along the integral curves of vector fields of another foliations. According to this idea, we define a new concept of stability between foliations. A…

Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…

R. Thom's gradient conjecture states that if a gradient flow of an analytic function converges to a limit, it does so along a unique limiting direction. In this paper, we extend and settle this conjecture in the context of infinite…

In this paper we use a dynamical approach to prove some new divergence theorems on complete non-compact Riemannian manifolds.