Results 41 to 50 of about 1,758 (174)

A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley   +1 more source

Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions

Mathematics
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations.
Andrei D. Polyanin, Alexander V. Aksenov
doaj   +1 more source

A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

, 2017
We prove the long time existence and uniqueness of solution to a parabolic Monge–Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t ...
Tao Zheng
core   +1 more source

Unitarily invariant valuations on convex functions

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Continuous, dually epi‐translation invariant valuations on the space of finite‐valued convex functions on Cn$\mathbb {C}^n$ that are invariant under the unitary group are investigated. It is shown that elements belonging to the dense subspace of smooth valuations admit a unique integral representation in terms of two families of Monge–Ampère ...
Jonas Knoerr
wiley   +1 more source

Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge-Ampère equation

, 2022
International audienceIn this paper, we establish a local regularity result for $W^{2,p}_{\mathrm{loc}}$ solutions to complex degenerate nonlinear elliptic equations $F(D^2_{\mathbb{C}} u)=f$ when they are comparable to the Monge-Ampère equation.Notably,
Abja, Soufian, Olive, Guillaume
core   +1 more source

Dimer models and conformal structures

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.
Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala, Erik Duse, István Prause, Xiao Zhong   +3 more
wiley   +1 more source

Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds [PDF]

, 2018
We show that a positive Borel measure of positive finite total mass, on a compact Hermitian manifold, admits a Hölder continuous quasi-plurisubharmonic solution to the Monge-Ampère equation if and only if it is dominated locally by Monge-Ampère measures ...
Nguyen, Ngoc Cuong, Kołodziej, Sławomir, Nguyen, Ngoc   +2 more
core   +1 more source

Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow

Discrete Dynamics in Nature and Society, 2020
In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to
Zenggui Wang
doaj   +1 more source

On the Existence of Solutions to a Bi-Planar Monge-Ampère Equation

, 2020
In this article, we consider a fully nonlinear partial differential equation which can be expressed as a sum of two Monge-Ampère operators acting in different two-dimensional coordinate sections.
Akramov, Ibrokhimbek, Oliver, Marcel
core   +1 more source

Inequalities and counterexamples for functional intrinsic volumes and beyond

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract We show that analytic analogs of Brunn–Minkowski‐type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saorín Gómez.
Fabian Mussnig, Jacopo Ulivelli
wiley   +1 more source