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math.AP2026
A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity
Qing Han, Jui-Yun Hung, Nan Wu
Inspired by a pioneering work by Caffarelli, Gidas, and Spruck, we study positive solutions to the Yamabe equation with nonremovable isolated singularities. It is known that there…
math.AP2026
A new approach to interior estimates for fully nonlinear elliptic equations
Jui-Yun Hung, Jiakun Liu, Neil Trudinger
We give new, elementary proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum pri…
math.AP2026
A Parametrization of Solutions to the Liouville Equation in a Punctured Disc
Qing Han, Jui-Yun Hung
In this paper, we study parametrization of solutions to the Liouville equation near their isolated singular points. We demonstrate that prescribing asymptotic behaviors forms a new…