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Geometric Pluripotential Theory on Sasaki Manifolds
We extend profound results in pluripotential theory on Kähler manifolds (Darvas in ar**v:1902.01982 , 2019) to Sasaki setting via its transverse...
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On the Lower Boundedness of Modified K-energy
In this paper we prove that the modified K -energy on a Fano manifold X is bounded from below if X admits a special degeneration whose central fiber...
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Lee–Yang–Fisher Zeros for the DHL and 2D Rational Dynamics, II. Global Pluripotential Interpretation
In a classical work of the 1950s, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic...
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The Eigenvalue Problem for the Complex Monge–Ampère Operator
We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge–Ampère operator on a...
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Pluripotential Numerics
We study the numerical approximation of the fundamental quantities in pluripotential theory , namely the Siciak Zaharjuta extremal plurisubharmonic...
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C-Robin functions and applications
We continue the study in [1] in the setting of pluripotential theory arising from polynomials associated to a convex body C in (ℝ + ) d . Here we discuss C ...
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A Variational Approach to the Eigenvalue Problem for Complex Hessian Operators
Let \(1 \leq m \leq n\) be two integers and...
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Geodesic Distance and Monge—Ampère Measures on Contact Sets
We prove a geodesic distance formula for quasi-psh functions with finite entropy, extending results by Chen and Darvas. We work with big and nef...
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Complex Hessian-Type Equations in the Weighted m-Subharmonic Class
We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure μ defined on an m -hype...
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A variational approach to the quaternionic Monge–Ampère equation
In this paper, we use the variational method to solve the quaternionic Monge–Ampère equation when the right-hand side is a positive measure of finite...
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Quaternionic Monge–Ampère Measure on Pluripolar Set
In this paper, we prove that in a hyperconvex domain Ω in ℍ n , if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure,...
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A Priori Estimate for the Complex Monge–Ampère Equation
In this paper, we use the Sobolev type inequality in Wang et al. (Moser–Trudinger inequality for the complex Monge–Ampère equation,
ar**v:2003.06056v1 ... -
Asymptotic Construction of the Optimal Degeneration for a Fano Manifold
Optimal degeneration is the algebraic counterpart of the prescribed geometric flow. We review some construction of the degeneration via the...
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Geometric Flow, Multiplier Ideal Sheaves and Optimal Destabilizer for a Fano Manifold
In (Donaldson in J Differ Geom 70(3):453–472, 2005), it was asked whether the lower bound of the Calabi functional is achieved by a sequence of the...
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Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations
In this paper, we study the relations between trace inequalities (Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity...
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Extremizers of the J Functional with Respect to the d1 Metric
In previous work, Darvas, George and Smith obtained inequalities between the large scale asymptotic of the J functional with respect to the d 1 metric...