相关论文: A Lefschetz formula for higher rank

For algebraic Anosov diffeomorphisms we first express the reduced leafwise cohomology with respect to the unstable foliation in terms of finite dimensional Lie algebra cohomology. We then prove a dynamical Lefschetz trace formula for the…

We prove that for continuous Lorentz-Finsler spaces timelike completeness implies inextendibility. Furthermore, we prove that under suitable locally Lipschitz conditions on the Finsler fundamental function the continuous causal curves that…

We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short intervals conditionally on the generalized Riemann…

A hyperelliptic broken Lefschetz fibration is a generalization of a hyperelliptic Lefschetz fibration. We construct and compute a local signature of hyperelliptic directed broken Lefschetz fibrations by generalizing Endo's local signature…

We show that compact locally symmetric Lorentz manifolds are geodesically complete.

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of…

In Hilbert space setting we prove local lipchitzness of projections onto parametric polyhedral sets represented as solutions to systems of inequalities and equations with parameters appearing both in left-hand-sides and right-hand-sides of…

We provide a Plancherel decomposition for the space of symplectic bilinear forms of rank $2n$ over a local non-archimedean field $F$ in terms of that of $GL_n(F)$.

In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function $\hat{\zeta}(s)$ (resp. the zeta function $\zeta_Y(s)$ of a smooth projective curve $Y$ over a finite field $\mathbb{F}_q$, $q=p^f$)) one…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action…

Consider a standard graded artinian $k$-algebra $B$ and an extension of $B$ by a new variable, $A=B\otimes_k k[x]/(x^d)$ for some $d\geq 1$. We will show how maximal rank properties for powers of a general linear form on $A$ can be…

Quickly convergent series are given to compute polyzeta numbers. The formula involves an intricate combination of (generalized) polylogarithms at 1/2. However, the combinatorics has a very simple geometric interpretation: it corresponds…

The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force…

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister…

A generalized harmonic map equation is presented based on the proposed action functional in the Weyl space (PLA, 135, 315, 1989).

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.

The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in a space by a ball. In nonpositively curved spaces, one can construct fillings using geodesics, but fillings become more complicated…

In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients…

For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-Sullivan measures, as well as a Dirichlet-type theorem and a…