14 citations · 66 across the 49 of their papers we have counts for
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The generalised Pólya conjecture for the Dirichlet eigenvalues
Genqian Liu
In this paper, we prove the Generalized Pólya conjecture for the Dirichlet eigenvalues. In other words, we show that $λ_k(α) \ge \frac{(2π)^α k^{α/n}}{\big(ω_n \cdot {vol}(Ω)\big)^…
Pólya conjecture for the Neumann eigenvalues
Genqian Liu
For a given bounded domain with -smooth boundary, we prove the Pólya conjecture for the Neumann eigenvalues. In other words, we prove that \begin{eqnarra…
Spectral invariants of the Stokes problem
Genqian Liu
For a given bounded domain with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated w…
Heat invariants of the perturbed polyharmonic Steklov problem
Genqian Liu
For a given bounded domain with smooth boundary in a smooth Riemannian manifold , we establish a procedure to get all the coefficients of the asymptotic expans…