Results 31 to 40 of about 141 (130)

Some applications and maximum principles for multi-term time-space fractional parabolic Monge-Ampère equation

Demonstratio Mathematica
This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative.
Guan Tingting, Wang Guotao, Araci Serkan
doaj   +1 more source

Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley   +1 more source

Quasibounded solutions to the complex Monge–Ampère equation

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract We study the Dirichlet problem for the complex Monge–Ampère operator on B‐regular domains in Cn$\mathbb {C}^n$, allowing boundary data that is singular or unbounded. We extend the concept of pluri‐quasibounded functions on the domain to functions on the boundary, defined by the existence of plurisuperharmonic majorants that dominate their ...
Mårten Nilsson
wiley   +1 more source

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

Exterior Dirichlet Problem for Translating Solutions of Gauss Curvature Flow in Minkowski Space

Abstract and Applied Analysis, 2014
We prove the existence of solutions to a class of Monge-Ampère equations on exterior domains in ℝn(n≥2) and the solutions are close to a cone. This problem comes from the study of the flow by powers of Gauss curvature in Minkowski space.
Hongjie Ju
doaj   +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

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

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

On uniqueness of solutions to complex Monge–Ampère mean field equations

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.
Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
wiley   +1 more source

A C 2,α,β estimate for complex Monge–Ampère type equations with conic sigularities

Advanced Nonlinear Studies
In this paper, we give an alternative approach to the C 2,α,β estimate for complex Monge-Ampère equations with cone singularities along simple normal crossing divisors.
Huang Liding, Tian Gang, Wang Jiaxiang
doaj   +1 more source