On the range of a class of complex Monge-Ampère operators on compact Hermitian manifolds [PDF]
Journal of Functional AnalysisYinji Li, Zhiwei Wang, Xiangyu Zhou
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Moser–Trudinger type inequalities for complex Monge–Ampère operators and Aubin’s “hypothèse fondamentale” [PDF]
Annales De La Faculté Des Sciences De Toulouse, 2022 Robert J Berman, Bo Berndtsson
exaly +2 more sources
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties [PDF]
, 2012 We show, using a direct variational approach, that the second boundary value problem for the Monge-Amp\`ere equation in R^n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P.
Berman, Robert J., Berndtsson, Bo
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Multi-physics Optimal Transportation and Image Interpolation [PDF]
, 2014 International audienceOptimal transportation theory is a powerful tool to deal with image interpolation. This was first investigated by Benamou and Brenier \cite{BB00} where an algorithm based on the minimization of a kinetic energy under a conservation ...
Hug, Romain +2 more
core +5 more sources
On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
, 2020 Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson ...
Xia, Mingchen
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Functions dividing their Hessian determinants and affine spheres [PDF]
, 2016 The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the function.
Fox, Daniel J. F.
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Free analysis and random matrices [PDF]
, 2016 We describe the Schwinger–Dyson equation related with the free difference quotient. Such an equation appears in different fields such as combinatorics (via the problem of the enumeration of planar maps), operator algebra (via the definition of a natural ...
Guionnet, Alice
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Two maximum principles for a nonlinear fourth order equation from thin plate theory [PDF]
, 2014 We develop two maximum principles for a nonlinear equation of fourth order that arises in thin plate theory. As a consequence, we obtain uniqueness results for the corresponding fourth order boundary value problem under Navier boundary conditions as ...
Danet, C.-P.
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Ricci flat K\"ahler metrics on rank two complex symmetric spaces [PDF]
, 2018 We obtain Ricci flat K\"ahler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space.
Biquard, Olivier, Delcroix, Thibaut
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Comparison of two notions of subharmonicity on non-archimedean curves
, 2018 We show that a continuous function on the analytification of a smooth proper algebraic curve over a non-archimedean field is subharmonic in the sense of Thuillier if and only if it is psh, i.e. subharmonic in the sense of Chambert-Loir and Ducros.
Wanner, Veronika
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