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math.AP2026
On the equality case in the Brunn-Minkowski inequality for the Monge-Ampère eigenvalue
Nam Q. Le
We characterize the equality case in the Brunn-Minkowski inequality for the Monge-Ampère eigenvalue of general bounded convex domains. This together with the author's previous wor…
math.AP2026
A Variational Approach to Degenerate Monge--Ampère Equations with Mixed Measures and Monotonicity
Nam Q. Le
We study the solvability and uniqueness for several degenerate Monge--Ampère equations including the Monge--Ampère eigenvalue problem in real Euclidean spaces that involve singul…
math.AP2024
Singular Abreu equations and linearized Monge-Ampère equations with drifts
Young Ho Kim, Nam Q. Le, Ling Wang +1
We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvab…