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math.DG2024
RC-positivity, Schwarz's lemma and comparison theorems
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps be…
math.CO2024
Eigenvalues of the Hodge Laplacian on digraphs
Alexander Grigor'yan, Yong Lin, S. -T. Yau +1
This paper aims to compute and estimate the eigenvalues of the Hodge Laplacians on directed graphs. We have devised a new method for computing Hodge spectra with the following two…