Guokuan Shao

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math.CV2026

Characterization of Sobolev regularity of plurisubharmonic functions

Hongrong Chen, Guokuan Shao, Wenxuan Wang

Let $f$ be a nonzero holomorphic germ at $0 \in C^{n}$ with $f (0) = 0$ , and let $χ$ be a $C^{2}$ non-decreasing convex function on the left half-line. We establish sharp necessar…

math.CV2024

Strong holomorphic Morse inequalities on non-compact complex manifolds with optimal fundamental estimate

Manli Liu, Guokuan Shao, Wenxuan Wang

In this paper, we establish strong holomorphic Morse inequalities on non-compact manifolds under the condition of optimal fundamental estimates. We show that optimal fundamental es…

math.CV2024

Asymptotics of Spectral Functions of Lower Energy Forms on Weakly 1-Complete Manifolds

Xiquan Peng, Guokuan Shao, Wenxuan Wang

In this paper, we show that the optimal fundamental estimate holds true on a weakly $1$ -complete manifold with mild conditions, then we establish the weak Morse inequalities for lo…