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On Liouville's theorem for the Hessian quotient equation
Siyuan Lu, Marcin Sroka
We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation in . The proof is based on the observation that after rewriting…
Pogorelov type interior estimate for Hessian quotient equation and its application
Siyuan Lu, Yi-Lin Tsai
In this paper, we derive a Pogorelov type interior estimate for the Hessian quotient equation . As an application, we show that convex v…
A simple proof of curvature estimates for the n-1 Hessian equation
Siyuan Lu, Yi-Lin Tsai
In [Amer. J. Math. 141 (2019), no. 5, 1281-1315], Ren and Wang proved the curvature estimates for the curvature equation. The purpose of this note is to give a simple proof o…
Interior estimate for Hessian quotient equation in general dimension
Siyuan Lu
In this paper, we study the interior regularity problem for the Hessian quotient equation . We give a complete answer to this longstandi…
Interior estimate for Hessian quotient equation in dimension three
Siyuan Lu
In this paper, we establish an interior estimate for the Hessian quotient equation in dimension three. A crucial ingredient in our proo…