Abstract : We solve the Bj\"{o}rling problem for zero mean curvature surfaces in the three-dimensional light cone. As an application, we construct and classify all rotational zero mean curvature surfaces.
Abstract : In this paper, we introduce a class of Moran measures generated by quasi periodic sequences, and consider power decay of the Fourier transforms of this kind of measures.
Abstract : In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.
Abstract : In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain \begin{equation*} -\Delta u+V(x)u-\frac{u}{\sqrt{1-u^2}}\Delta \sqrt{1-u^2}=\lambda |u|^{p-2}u,\ x\in\mathbb{R}^{N}, \end{equation*} where $2\leq p<2^*, N\geq 3$. By the Ekeland variational principle, the cut off technique, the change of variables and the $L^{\infty}$ estimate, we study the existence of positive solutions. Here, we construct the $L^{\infty}$ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.
Abstract : For a finite subgroup $G$ of $GL_n(\mathbb C)$, the moduli space $\mathcal M_{\theta}$ of $\theta$-stable $G$-constellations is rarely smooth. This note shows that for a group $G$ of type $\frac{1}{r}(1,a,b)$ with $r=abc+a+b$, there is a generic stability parameter $\theta\in \Theta$ such that the birational component $Y_{\theta}$ of $\theta$-stable $G$-constellations provides a resolution of the quotient singularity $X:=\mathbb C^3/G$.
Abstract : In this paper, we characterize amphicheiral 2-bridge knots with symmetric union presentations and show that there exist infinitely many amphicheiral 2-bridge knots with symmetric union presentations with two twist regions. We also show that there are no amphicheiral 3-stranded pretzel knots with symmetric union presentations.
Abstract : For a knot in the $3$--sphere, the Upsilon invariant is a piecewise linear function defined on the interval $[0,2]$. It is known that this invariant of an L--space knot is the Legendre--Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L--space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L--space knot is a convex conjugate of a gap function.
Bikash Chakraborty
Bull. Korean Math. Soc. 2022; 59(5): 1247-1253
https://doi.org/10.4134/BKMS.b210700
Zhengmao Chen
Bull. Korean Math. Soc. 2023; 60(4): 1085-1100
https://doi.org/10.4134/BKMS.b220531
Seungsu Hwang, Gabjin Yun
Bull. Korean Math. Soc. 2022; 59(5): 1167-1176
https://doi.org/10.4134/BKMS.b210671
Tahire Ozen
Bull. Korean Math. Soc. 2023; 60(6): 1463-1475
https://doi.org/10.4134/BKMS.b220573
Yong Lin, Yuanyuan Xie
Bull. Korean Math. Soc. 2022; 59(3): 745-756
https://doi.org/10.4134/BKMS.b210445
Vu Trong Luong, Nguyen Duong Toan
Bull. Korean Math. Soc. 2024; 61(1): 161-193
https://doi.org/10.4134/BKMS.b230068
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2022; 59(5): 1317-1325
https://doi.org/10.4134/BKMS.b210759
Joungmin Song
Bull. Korean Math. Soc. 2022; 59(3): 609-615
https://doi.org/10.4134/BKMS.b210096
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