Research
Research
Research
Research
2,754+ open-access research outputs.
The holomorphy conjecture for suspensions of plane curve singularities and the holomorphy and monodromy conjectures for L\^e-Yomdin singularities of surfaces are proved. The first part of this paper…
We study $C_0$-semigroups on UMD Banach spaces under the assumption that a single semigroup operator admits a lower bound. We establish boundedness of $H^\infty$ functional calculi for the negative ge…
The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. We prove that $r_4(5,n)\ge 2^{2^{…
This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In thi…
In this paper, we show that starting from a geodesic ball $\overline{B_{r_0}}(0)$ in $\mathbb{H}^n$, for $n\geq3$, with prescribed non-decreasing rotationally symmetric mean curvature and the fixed co…
In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. …
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao o…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifica…
To any Jordan curve one may associate a circle homeomorphism $\varphi : \mathbb S^1 \to \mathbb S^1$ via conformal welding. Through this correspondence, the Loewner energy $I^L$, also known as the uni…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are…
We show for $\kappa \in (4,8)$ that the canonical conformally covariant measure on the conformal loop ensemble (CLE$_\kappa$) gasket, previously constructed indirectly by the first co-author and Schou…
We study Poincare-Sobolev type inequalities for compactly supported smooth functions which are defined in the Euclidean $n$-space and whose absolute value of gradient are Choquet $\delta /n$-integrabl…
In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(\kappa)$, as $\kappa \to 0$, with good rate function…
Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P…
We prove that every ordinal $\alpha<\omega_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive…
In this article, we address the lower bounds for the sums $a_f(p)+a_g(p)$ of the $p$-th Fourier coefficients of two twist-inequivalent, non-CM normalized newforms $f$ and $g$. Our main result shows th…
Given an $r$-uniform hypergraph $H$ and a positive integer $n$, the weak saturation number $\mathrm{wsat}(n,H)$ is the minimum number of edges in an $r$-uniform hypergraph $F$ on $n$ vertices such tha…
For a graph $G$, the general reduced second Zagreb index is defined as $$GRM_\lambda (G) = \sum_{uv \in E} (deg(u) + \lambda) (deg(v) + \lambda),$$ where $\lambda$ is an arbitrary real number and $deg…
The limited augmented Zarankiewicz number $z_L(m,n)$ satisfies $\operatorname{BSR}(m,n)\ge z_L(m,n)\ge z(m,n)$, where $\operatorname{BSR}(m,n)$ is the maximum SOS rank of $m\times n$ biquadratic forms…
We study the complexity of inverse cellular automata on configurations of bounded size. Deciding injectivity in this setting is co-NP-complete by a theorem of Durand. We give a simpler proof of this t…
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