Related papers: A Lefschetz fixed point formula for singular arith…

Consider a compact K\"ahler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this…

We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)

We present a simplified way to construct the Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ related to a $1$-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of…

We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…

A well-known theorem of W. Fischer and H. Grauert states that analytic fiber spaces with all fibers isomorphic to a fixed compact connected complex manifold are locally trivial. Motivated by this result, we show that if $k$ is an…

In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…

In this paper, we define the notion of graph trace kernels as a generalization of trace kernels. We associate a microlocal Lefschetz class with a graph trace kernel and prove that this class is functorial with respect to the composition of…

Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for hyperelliptic Lefschetz fibrations, and show that any hyperelliptic Lefschetz fibration…

In this article, we use $\lambda$-sequences to derive common fixed points for a family of self-mappings defined on a complete $G$-metric space. We imitate some existing techniques in our proofs and show that the tools emlyed can be used at…

We show that every continuous rotative mapping on a closed interval has a fixed point. This gives an answer to some open questions raised by Goebel and Koter.

We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…

An explicit formula for analytic torsion forms for fibrations by projective curves is given. In particular one obtains a formula for direct images in Arakelov geometry in the corresponding setting. The main tool is a new description of…

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.

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…

For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the…

This memoir is devoted to the study of formal-analytic arithmetic surfaces. These are arithmetic counterparts, in the context of Arakelov geometry, of germs of smooth complex-analytic surfaces along a projective complex curve.…

We prove fixed points results for sandpiles starting with arbitrary initial conditions. We give an effective algorithm for computing such fixed points, and we refine it in the particular case of SPM.

In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Sz\'ekelyhidi-Tosatti-Weinkove (TW17, TW19, STW17) by the study of the…

We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the…

We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…