اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn fully nonlinear CR invariant equations on the Heisenberg group
205
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author (2003). We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.
قيم البحث
اقرأ أيضاً
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a conjecture by Ga
uduchon which extends the Calabi conjecture; this was one of the original motivations to this work. We were also motivated by the fact that there had been increasing interests in fully nonlinear pdes from complex geometry in recent years, and aimed to develop general methods to cover as wide a class of equations as possible.
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.
Let $(Sigma,g)$ be a closed Riemannian surface, $textbf{G}={sigma_1,cdots,sigma_N}$ be an isometric group acting on it. Denote a positive integer $ell=inf_{xinSigma}I(x)$, where $I(x)$ is the number of all distinct points of the set ${sigma_1(x),cdot
s,sigma_N(x)}$. A sufficient condition for existence of solutions to the mean field equation $$Delta_g u=8piellleft(frac{he^u}{int_Sigma he^udv_g}-frac{1}{{rm Vol}_g(Sigma)}right)$$ is given. This recovers results of Ding-Jost-Li-Wang (Asian J Math 1997) when $ell=1$ or equivalently $textbf{G}={Id}$, where $Id$ is the identity map.
In this paper we consider a class of fully nonlinear equations which cover the equation introduced by S. Donaldson a decade ago and the equation introduced by Gursky-Streets recently. We solve the equation with uniform weak $C^2$ estimates, which hold for degenerate case.
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perrons method. If the equation is uniformly e
lliptic in the sense of cite{SS}, we prove the discontinuous viscosity solution is Holder continuous and thus it is a viscosity solution.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
