相关论文: Dual mixed volumes and isosystolic inequalities

Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…

We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…

We use a new approach that we call unification to prove that standard weighted double bubbles in $n$-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for…

We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group $G$ is…

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a…

A description of a large system of particles is often sought in a derivation from the detailed behaviour of just a few of the particles. The present thesis deals with the connection between such microscopic features and the nature of a…

The present article presents geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjoint orbit of an infinite-dimensional Lie group constructed…

We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven…

Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, combinatorial mixed valuations reflect and often inherit…

We consider two well-known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given…

In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy…

We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. As applications, we give a short, "euclidean" proof of the anisotropic Sobolev inequality and describe an anisotropic tube formula for…

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem…

In this article we discuss some aspects of double field theory cosmology with an emphasis on the role played by the dilaton. The cosmological solutions of double field theory equations of motion after coupling a shifted dilaton to them are…

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…

A set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps "waves" on a riemannian symmetric space to "waves" on its dual riemannian…

In contact geometry, a systolic inequality is a uniform upper bound on the shortest period of a closed Reeb orbit, in terms of the contact volume. We prove a general systolic inequality valid on Seifert bundles with non-zero Euler number…

Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating cylindrical annulus with conical caps is considered with the aim to establish whether a small fraction of compositional buoyancy added to the…

We have identified an important source of mixing in stellar radiation zones, that would arise whenever two conditions are satisfied: (1) the presence of an inverse vertical compositional gradient, and (2) the presence of…

We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement…