相关论文: On the upper semicontinuity of the Wu metric
We discuss the properties of the Wu pseudometric and present counterexamples for its upper semicontinuity that answers the question posed by Jarnicki and Pflug. We also give formulae for the Wu pseudometric in elementary Reinhardt domains.
We give a quick direct proof of Wu's theorem on the subadditivity of Hermitian metrics of negative holomorphic sectional curvature.
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
We consider semi-continuity of certain dimensions on group schemes.
We discuss some basic properties of the Sibony functions and pseudometrics.
We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.
We show a continuity result for the Weyl pseudometric on subshifts which are generated by model sets. This fact is then used for multiple constructions of subshifts that exhibit different behavior regarding entropy, amorphic complexity and…
We discuss some aspects of the theory of subelliptic estimates.
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
We establish sufficient conditions for the upper semicontinuity and the continuity of the entropy of Sinai probability measures invariant by partially hyperbolic diffeomorphisms and discuss their application in several examples.
We prove that for $\mathcal{C}^{1,\alpha}$ diffeomorphisms on a compact manifold $M$ with ${\rm dim} M\leq 3$, if an invariant measure $\mu$ is a continuity point of the sum of positive Lyapunov exponents, then $\mu$ is an upper…
Some observations on the Wu-Sprung potential.
We study the Wu metric for the non-convex domains of the form \[ E_{2m} = \big\{ z \in \mathbb{C}^n : \vert z_1 \vert^{2m} + \vert z_2 \vert^2 + \ldots + \vert z_{n-1} \vert^2 + \vert z_n \vert^{2} <1 \big \}, \] where $ 0 < m < 1/2$.…
We study the Wu metric on convex egg domains of the form \[ E_{2m} = \big\{ z \in \mathbb{C}^n : \vert z_1 \vert^{2m} + \vert z_2 \vert^2 + \ldots + \vert z_{n-1} \vert^2 + \vert z_n \vert^{2} <1 \big\} \] where $m \geq 1/2, m \neq 1$. The…
For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, this paper establishes the upper semi-continuity of the…
We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…
A fundamental challenge within the metric theory of continued fractions involves quantifying sets of real numbers, when represented using continued fractions, exhibit partial quotients that grow at specific rates. For any positive function…
Let $S$ be a seminorm on an infinite-dimensional real or complex vector space $X$. Our purpose in this note is to study the continuity and discontinuity properties of $S$ with respect to certain norm-topologies on $X$.
This paper attempts to study the continuity of the Hurwitz metric in arbitrary proper subdomains of the complex plane and to introduce a new invariant metric bi-Lipschitz equivalent to the Hurwitz metric in hyperbolic domains. The lower…
In this article, we give an upper bound estimate for the quantitative loss of the upper semi-continuity of the metric entropy for $C^r\:(r>1)$ diffeomorphisms. Building on earlier entropy estimates and reparametrization methods, we optimize…