Related papers: Boundary regular fixed points in Loewner theory
A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is…
We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe…
We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of $C^2$…
Consider a parameter dependent vector field on either Euclidean space or a compact Riemannian manifold. Suppose that it possesses a parameter dependent initial condition and a parameter dependent stable hyperbolic equilibrium point. It is…
We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…
We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.
In a paper from 1960, Felix Browder established a theorem concerning the continuation of the fixed points of a family of continuous functions $f_t:X\to X$ depending continuously on a parameter $t\in [0,1]$, where $X$ is a convex and compact…
We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in \cite{bcr}. Our main assumption is an appropriate…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
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…
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local…
We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.
In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the higher regularity of the free boundaries in obstacle-type…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the…
We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss…
Let $H$ be a composition of an $\mathbb{R}$-linear planar mapping and $z\mapsto z^n$. We classify the dynamics of $H$ in terms of the parameters of the $\mathbb{R}$-linear mapping and the degree by associating a certain finite Blaschke…
We establish existence and regularity results for boundary value problems arising from the first variation of the Willmore energy in the graphical setting. Our focus lies on two-dimensional surfaces with fixed clamped boundary conditions,…
This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is…