9 citations · 23 across the 16 of their papers we have counts for
17 papers
Asymptotics for the -Hessian Eigenvalue on the Unit Ball
Nicholas McCleerey, Abhinav Pande, Thidas Wanasinghe
We compute the limit of the eigenvalue of the -Hessian operator on the unit ball in when , assuming that the ratio remains fixe…
Some variational problems for the complex Monge--Amp{è}re operator
Jianchun Chu, Yaxiong Liu, Nicholas McCleerey +1
We consider the Dirichlet problem for the complex Monge--Ampère equation on strongly pseudoconvex Kähler manifolds when the right-hand side is decreasing in the solution. Using flo…
Lines in the space of Kähler metrics
Tamás Darvas, Nicholas McCleerey
We establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. We construct a wide range of weak geodesic lines on arbitrary pr…
Asympotitcs for Some Singular Monge-Ampère Equations
Nicholas McCleerey
Given a psh function and a smooth, bounded , it is known that one can solve the Monge-Ampère equation , with some…
Regularity of the solution to a real Monge--Ampère equation on the boundary of a simplex
Rolf Andreasson, Jakob Hultgren, Mattias Jonsson +2
Motivated by conjectures in Mirror Symmetry, we continue the study of the real Monge--Ampère operator on the boundary of a simplex. This can be formulated in terms of optimal trans…
The Eigenvalue Problem for the Complex Hessian Operator on -Pseudoconvex Manifolds
Jianchun Chu, Yaxiong Liu, Nicholas McCleerey
We establish -regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly -pseudoconvex manifolds, along with a variational formula…
Singularities of the solution to a Monge--Ampère equation on the boundary of the 3-simplex
Mattias Jonsson, Nicholas McCleerey, Neil Patram +1
We show that the metric defined by the solution to the tropical Monge-Ampère equation, as defined by Hultgren, Mazzon, and the first two authors, on the boundary of the 3-simplex i…
Geodesic Rays in the Donaldson--Uhlenbeck--Yau Theorem
Mattias Jonsson, Nicholas McCleerey, Sanal Shivaprasad
We give new proofs of two implications in the Donaldson--Uhlenbeck--Yau theorem. Our proofs are based on geodesic rays of Hermitian metrics, inspired by recent work on the Yau--Tia…
Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
Jakob Hultgren, Mattias Jonsson, Enrica Mazzon +1
For a class of maximally degenerate families of Calabi-Yau hypersurfaces of complex projective space, we study associated non-Archimedean and tropical Monge-Ampère equations, takin…
Lelong Numbers of -Subharmonic Functions Along Submanifolds
Jianchun Chu, Nicholas McCleerey
We study the possible singularities of an -subharmonic function along a complex submanifold of a compact Kähler manifold, finding a maximal rate of growth for which…
Plurisupported Currents on Compact Kähler Manifolds
Nicholas McCleerey
Let be a compact Kähler manifold. We study plurisupported currents on , i.e. closed, positive -currents which are supported on a pluripolar set. In particular, we are…
Fully non-linear degenerate elliptic equations in complex geometry
Jianchun Chu, Nicholas McCleerey
We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of…
Volume of Perturbations of Pseudoeffective Classes
Nicholas McCleerey
In this short note, we consider the question of determining the asymptotics of the volume function near the boundary of the pseudoeffective cone on compact Kähler manifolds. We sol…
regularity of geodesics of singular Kähler metrics
Jianchun Chu, Nicholas McCleerey
We show the optimal regularity of geodesics in nef and big cohomology class on Kähler manifolds away from the non-Kähler locus, assuming sufficiently regular initial data…
Envelopes with Prescribed Singularities
Nicholas McCleerey
We prove that quasi-plurisubharmonic envelopes with prescribed analytic singularities in suitable big cohomology classes on compact Kähler manifolds have the optimal regu…
Pluricomplex Green's functions and Fano manifolds
Nicholas McCleerey, Valentino Tosatti
We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities…
Polar Transform and Local Positivity for Curves
Nicholas McCleerey, Jian Xiao
Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local posi…