A remark on the quaternionic Monge-Ampère equation on foliated manifolds
نویسندگان
چکیده
Pursuing the approach of Gentili and Vezzoni [Math. Res. Not. IMRN 12 (2022), pp. 9499–9528] we study quaternionic Monge-Ampère equation on HKT (hyperkähler with torsion) manifolds admitting an foliation having corank 4 4 . We show that in this setting has always a unique solution for every basic datum. This includes alttext="upper S upper U left-parenthesis 3 right-parenthesis"> SU ( 3 stretchy="false">) encoding="application/x-tex">\operatorname {SU}(3)
منابع مشابه
Quaternionic Monge-ampère Equations
The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in H. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].
متن کاملA note on Monge-Ampère Keller-Segel equation
This note studies the Monge–Ampère Keller–Segel equation in a periodic domain Td(d ≥ 2), a fully nonlinear modification of the Keller–Segel equation where the Monge–Ampère equation det(I + ∇2v) = u + 1 substitutes for the usual Poisson equation ∆v = u. The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in L∞ 0, T ;L∞ ∩W 1,1+γ(Td) ...
متن کاملContinuity Estimates for the Monge-Ampère Equation
In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semi-geostrophic equation arising in meteorology.
متن کاملQuaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds
A quaternionic version of the Calabi problem on the MongeAmpère equation is introduced, namely a quaternionic MongeAmpère equation on a compact hypercomplex manifold with an HKT-metric. The equation is non-linear elliptic of second order. For a hypercomplex manifold with holonomy in SL(n,H), uniqueness (up to a constant) of a solution is proven, as well as the zero order a priori estimate. The ...
متن کاملEinstein - Weyl structures on complex manifolds and conformal version of Monge - Ampère equation
A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2022
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/16121