Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2024-03-01
Positive solutions to discrete harmonic functions in unbounded cylinders
Fengwen Han, Lidan WangAbstract : In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in $\mathbb{Z}^d$. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.
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2024-03-01
Remarks on Ulrich bundles of small ranks over quartic fourfolds
Yeongrak KimAbstract : In this paper, we investigate a few strategies to construct Ulrich bundles of small ranks over smooth fourfolds in $\mathbb{P}^5$, with a focus on the case of special quartic fourfolds. First, we give a necessary condition for Ulrich bundles over a very general quartic fourfold in terms of the rank and the Chern classes. Second, we give an equivalent condition for Pfaffian fourfolds in every degree in terms of arithmetically Gorenstein surfaces therein. Finally, we design a computer-based experiment to look for Ulrich bundles of small rank over special quartic fourfolds via deformation theory. This experiment gives a construction of numerically Ulrich sheaf of rank $4$ over a random quartic fourfold containing a del Pezzo surface of degree $5$.
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2023-03-01
The gradient flow equation of Rabinowitz action functional in a symplectization
Urs FrauenfelderAbstract : Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.
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2024-03-01
Real hypersurfaces in the complex hyperbolic quadric with cyclic parallel structure Jacobi operator
Jin Hong Kim, Hyunjin Lee, Young Jin SuhAbstract : Let $M$ be a real hypersurface in the complex hyperbolic quadric~${Q^{m}}^{*}$, $m \geq 3$. The Riemannian curvature tensor field~$R$ of~$M$ allows us to define a symmetric Jacobi operator with respect to the Reeb vector field~$\xi$, which is called the structure Jacobi operator~$R_{\xi} = R(\, \cdot \, , \xi) \xi \in \text{End}(TM)$. On the other hand, in~\cite{Semm03}, Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator~$R_{\xi}$ for a real hypersurface~$M$ in the complex hyperbolic quadric~${Q^{m}}^{*}$. Furthermore, we give a complete classification of Hopf real hypersurfaces in ${Q^{m}}^{*}$ with such a property.
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2024-03-01
A note on Sobolev type trace inequalities for $s$-harmonic extensions
Yongrui Tang, Shujuan ZhouAbstract : In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.
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2024-03-01
Conics in quintic del Pezzo varieties
Kiryong Chung, Sanghyeon LeeAbstract : The smooth quintic del Pezzo variety $Y$ is well-known to be obtained as a linear sections of the Grassmannian variety $\mathrm{Gr}(2,5)$ under the Pl\"ucker embedding into $\mathbb{P}^{9}$. Through a local computation, we show the Hilbert scheme of conics in $Y$ for $\text{dim} Y \ge 3$ can be obtained from a certain Grassmannian bundle by a single blowing-up/down transformation.
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2022-11-01
$\mathbb{D}$-solutions of BSDEs with Poisson jumps
Imen HassairiAbstract : In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class $\mathbb{D}$.
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The Difference of Hyperharmonic Numbers via Geometric and Analytic Methods
\c{C}a\u{g}atay Altunta\c{s}
, Haydar G\"{o}ral, Do\u{g}a Can Sertba\c{s}J. Korean Math. Soc. 2022; 59(6): 1103-1137
https://doi.org/10.4134/JKMS.j210630 -
Cup product on relative bounded cohomology
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345 -
Pseudo-Riemannian Sasaki solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
J. Korean Math. Soc. 2023; 60(1): 115-141
https://doi.org/10.4134/JKMS.j220232 -
New congruences for $\ell$-regular overpartitions
Ankita Jindal, Nabin K. Meher
J. Korean Math. Soc. 2022; 59(5): 945-962
https://doi.org/10.4134/JKMS.j220011
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Rigidity and nonexistence of Riemannian immersions in semi-Riemannian warped products via parabolicity
Railane Antonia, Henrique de Lima, Márcio Santos
J. Korean Math. Soc. 2024; 61(1): 41-63
https://doi.org/10.4134/JKMS.j220523 -
Some abelian McCoy rings
Rasul Mohammadi, Ahmad Moussavi, masoome zahiri
J. Korean Math. Soc. 2023; 60(6): 1233-1254
https://doi.org/10.4134/JKMS.j220625 -
An intrinsic proof of Numata's theorem on Landsberg spaces
Salah Gomaa Elgendi, Amr Soleiman
J. Korean Math. Soc. 2024; 61(1): 149-160
https://doi.org/10.4134/JKMS.j230263 -
Geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one
Sang-Bum Yoo
J. Korean Math. Soc. 2024; 61(1): 161-181
https://doi.org/10.4134/JKMS.j230278
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