Results 11 to 20 of about 112,001 (232)
The Pontryagin Forms of Hessian Manifolds [PDF]
The pontryagin forms of hessian manifolds, 2015 We show that Hessian manifolds of dimensions 4 and above must have vanishing Pontryagin forms. This gives a topological obstruction to the existence of Hessian metrics. We find an additional explicit curvature identity for Hessian 4-manifolds. By contrast, we show that all analytic Riemannian 2-manifolds are Hessian.
John Armstrong, Shun-ichi Amari
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Complex Hessian Equations on Some Compact Kähler Manifolds [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f:M→ℝ and an integer ...
Asma Jbilou
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The lower bounds of the first eigenvalues for the biharmonic operator on manifolds [PDF]
Journal of Inequalities and Applications, 2016 In this paper, we use the Reilly formula and the Hessian comparison theorem to estimate the lower bounds of the first eigenvalues for the biharmonic operator eigenvalue problems (buckling problem and clamped plate problem) on manifolds.
Liuwei Zhang, Yan Zhao
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Golden and Metallic Structures on Hessian Manifolds
MathematicsWe consider the reciprocal cost function J(x)=12(x+x−1)−1 and its n-dimensional extension J(x1,…,xn)=12(R+R−1)−1,R=∏i=1nxiαi,α=(α1,…,αn)∈Rn∖{0}. In logarithmic coordinates ti=logxi, the Hessian of J has a rank of one at every point.
Jonathan Washburn, Milan Zlatanović
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Monge-Ampère equations on compact Hessian manifolds
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZEWe consider degenerate Monge-Ampère equations on compact Hessian manifolds. We establish compactness properties of the set of normalized quasi-convex functions and show local and global comparison principles for twisted Monge-Ampère operators. We then use the Perron method to solve Monge-Ampère equations whose RHS involves an arbitrary probability ...
Guedj, Vincent, Tô, Tat Dat
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Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds [PDF]
, 2023 peer reviewedIn this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat semigroups on Riemannian manifolds. Our approach extends the Hessian formulas established by Stroock (1996) and removes in particular the ...
Cheng, Li-Juan +5 more
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Degenerate complex Hessian equations on compact Hermitian manifolds
, 2023 International audienceIn this note we provide uniform a priori estimates for solutions to degenerate complex Hessian equations on compact hermitian manifolds.
Guedj, Vincent, Lu, Chinh H.
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Homogeneous hessian manifolds [PDF]
Annales de l'Institut Fourier, 1980 A flat affine manifold is said to Hessian if it is endowed with a Riemannian metric whose local expression has the form g i j
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Curvature of Hessian manifolds
Differential Geometry and its Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Amari, J. Armstrong
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Homology Groups in Warped Product Submanifolds in Hyperbolic Spaces
Journal of Mathematics, 2021 In this paper, we show that if the Laplacian and gradient of the warping function of a compact warped product submanifold Ωp+q in the hyperbolic space ℍm−1 satisfy various extrinsic restrictions, then Ωp+q has no stable integral currents, and its ...
Yanlin Li +3 more
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