We determine the radii of concavity for the classes $\mathcal{S}_e^*$ and $\mathcal{C}_e$ of univalent functions associated with the exponential mapping $e^z$. Under the geometric framework of Avkhadiev--Wirths for conformal mappings with unbounded convex complements of opening angle $\pi A$ ($A \in (1,2]$), the radii are characterized by explicit transcendental equations. Sharpness is established globally by constructing explicit univalent extremal functions related to the disk automorphism $\omega_0(z) = -z$, and the strict monotonicity of these radii with respect to the parameter $A$ is verified numerically.
We study the boundary geometry of the Noshiro--Warschawski class $\mathcal{R}$. Using the geometric structure of close-to-convex domains and their relation to Loewner chains, we investigate the boundary behavior of functions in $\mathcal{R}$. In particular, we discuss the relation between spherical length and local con...
Shota Hoshinaga, I. Hotta, Li-Mei Wang· 0 citations
For every number field $K$, we prove the dynamical uniform boundedness conjecture for the unicritical family of polynomials $z^d + c$ when $d \geq 4$, and when $d = 3$ if $\mathbb{Q}(\sqrt{-3}) \not\subset K$. Furthermore, the unconditional bounds that we construct for periodic points of unicritical polynomials are eff...
We prove $C^{k/2,\alpha/2}$ -regularity up to a non-umbilic elliptic complex point for the Bishop family of holomorphic discs with boundary in a $C^{k,\alpha}$ regular real surface. Furthermore, we prove existence and regularity of holomorphic discs near certain complex points of index $\ge 2$. The proof employs a nove...
A basic property of holomorphic functions $f:D\to \mathbb{C}$ defined on domains $D$ of $\mathbb{C}$ is that $f$ is uniquely determined by its real part up to an additive constant. The same is true for slice regular functions defined on circular slice domains of the division algebra of quaternions or octonions. The aim...
We prove that a complete noncompact K\"ahler surface with nonnegative Ricci and nonnegative quadratic orthogonal bisectional curvature is contractible, and hence homeomorphic to $\mathbb{R}^4$, if it is simply connected at infinity. Under positive bisectional curvature, this removes the contractibility assumption from...
We completely characterize when a general curve of genus $g$ admits a non-degenerate degree $d$ map to projective space $\mathbb{P}^r$, that is $k$-secant along a linear space $\mathbb{P}^s \subset \mathbb{P}^r$ and deforms in a smooth family of expected dimension. This gives an optimal improvement of a theorem of Fark...
Alessio Cela, Carl Lian· 0 citations
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