Zobrazeno 1 - 10
of 108
pro vyhledávání: '"Czyż, Rafał"'
Autor:
Åhag, Per, Czyż, Rafał
This study extends the celebrated volume-capacity estimates of Dinew and Kolodziej, providing a foundation for examining the regularity of solutions to boundary value problems for complex Hessian equations. By integrating the techniques established b
Externí odkaz:
http://arxiv.org/abs/2409.16848
We initiate the study of $m$-subharmonic functions with respect to a semipositive $(1,1)$-form in Euclidean domains, providing a significant element in understanding geodesics within the context of complex Hessian equations. Based on the foundational
Externí odkaz:
http://arxiv.org/abs/2405.04948
This study examines geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains in $\mathbb{C}^n$. We establish that solutions possessing comparable singularities to the complex Monge-Amp\`ere equation are ident
Externí odkaz:
http://arxiv.org/abs/2405.04384
This study delves into the complex branches of a generalized Lambert $W$ function associated with $p,q$-binomial coefficients. We thoroughly analyze the multi-valued inverse of $\sinh(az)e^z$ under varying conditions for parameter $a$. This examinati
Externí odkaz:
http://arxiv.org/abs/2306.16362
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneou
Externí odkaz:
http://arxiv.org/abs/2306.13391
With only a complete solution in dimension one and partially solved in dimension two, the Lenz-Ising model of magnetism is one of the most studied models in theoretical physics. An approach to solving this model in the high-dimensional case ($d>4$) i
Externí odkaz:
http://arxiv.org/abs/2304.09815
Autor:
Ahag, Per, Czyz, Rafal
This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the $m$-Hessian measure that belongs to $L^q$, for $q\leq\frac nm$.
Externí odkaz:
http://arxiv.org/abs/2110.02620
Autor:
Ahag, Per, Czyz, Rafal
We construct a family of quasimetric spaces in generalized potential theory containing $m$-subharmonic functions with finite $(p,m)$-energy. These quasimetric spaces will be viewed both in $\mathbb{C}^n$ and in compact K\"ahler manifolds, and their c
Externí odkaz:
http://arxiv.org/abs/2110.02611
Autor:
Ahag, Per, Czyz, Rafal
With inspiration from the K\"ahler geometry, we introduce a metric structure on the energy class, $\mathcal{E}_{1,m}$, of $m$-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to
Externí odkaz:
http://arxiv.org/abs/2110.02604
Autor:
Ahag, Per, Czyz, Rafal
By proving an estimate of the sublevel sets for $(\omega,m)$-subharmonic functions we obtain a Sobolev type inequality that is then used to characterize the degenerate complex Hessian equations for such functions with bounded $(p,m)$-energy.
Externí odkaz:
http://arxiv.org/abs/2003.06157