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On finite-energy solutions of Kazan-Warner equations on the lattice graph
Huyuan Chen, Bobo hua
https://arxiv.org/abs/2509.01155 https://arxiv.org/pdf/2509…

On finite-energy solutions of Kazan-Warner equations on the lattice graph
We investigate finite-energy solutions to Kazdan-Warner type equations in 2-dimensional integer lattice graph $$ - Δu= \varepsilon e^{κu} +βδ_0\quad {\rm in}\ \mathbb{Z}^2,$$ where $\varepsilon=\pm1$, $κ>0$ and $β\in\mathbb{R}$. When $\varepsilon=1$, we prove the existence of a continuous family of finite-energy solutions for some parameter $κ$. This provides a partial resolution of the open problem on the existence of finite-energy solutions to the Liouville equation. When $\varepsi…

A Parallel Transport Frame Field Approach to Soliton Surfaces associated with the Betchov-Da Rios Equation in Four Space
Mustafa Altin, Ahmet Kazan
https://arxiv.org/abs/2507.06248

A Parallel Transport Frame Field Approach to Soliton Surfaces associated with the Betchov-Da Rios Equation in Four Space
In the present paper, the geometric properties of a soliton surface $Ψ=Ψ(s,t)$ associated with the Betchov-Da Rios (B-DR) equation using the parallel transport frame field in four-dimensional Euclidean space are examined. We obtain the derivative formulas for the parallel transport frame field of a unit-speed $s$-parameter curve $Ψ=Ψ(s,t),$ for all $t$. We obtain the soliton surface's two basic geometric invariants, $k$ and $h,$ and some other important invariants such as Gaussian curvature…

The Films, Theatre and Political Life of Elia Kazan
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updated: Thursday, June 26, 2025 - 9:38amfull name / name of organization: William Thomas…
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