Results 41 to 50 of about 159 (135)
Regularity of optimal mapping between hypercubes
Advanced Nonlinear Studies, 2023 In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri.
Chen Shibing, Liu Jiakun, Wang Xu-Jia
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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
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Aleksandrov-type estimates for a parabolic Monge-Ampere equation
Electronic Journal of Differential Equations, 2005 A classical result of Aleksandrov allows us to estimate the size of a convex function $u$ at a point $x$ in a bounded domain $Omega$ in terms of the distance from $x$ to the boundary of $Omega$ if $$int_{Omega} det D^{2}u , dx less than infty ...
David Hartenstine
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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
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Some applications of canonical metrics to Landau–Ginzburg models
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract It is known that a given smooth del Pezzo surface or Fano threefold X$X$ admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations).
Jacopo Stoppa
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Smooth approximation of twisted Kähler-Einstein metrics
Advanced Nonlinear Studies, 2023 In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.
Jin Lize, Wang Feng
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Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
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Soft Kirigami Composites for Form‐Finding of Fully Flexible Deployables
Advanced Materials Technologies, Volume 9, Issue 1, January 8, 2024.A new class of thin flexible structures are introduced that morph from flat into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are coupled: strain mismatch (inspired by biological growth) and kirigami cuts.
Jan Zavodnik +4 more
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Extended symmetry of the Witten-Dijkgraaf-Verlinde-Verlinde equation of Monge-Ampere type [PDF]
Opuscula MathematicaWe construct the Lie algebra of extended symmetry group for the Monge-Ampere type Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. This algebra includes novel generators that are unobtainable within the framework of the classical Lie approach and ...
Patryk Sitko, Ivan Tsyfra
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The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
Anais da Academia Brasileira de Ciências, 2008 In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1.
Shuguo Shi
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