6 papers · 1 filter
Graph statistics: An emerging discipline in non-Euclidean data analysis
Rongling Wu, Shing-Tung Yau
The explosive growth of complex data has catalyzed the emergence of graph statistics as a fundamentally new discipline in data science. Unlike traditional statistics, which operate…
Iterative construction of Hermitian-Einstein metrics on stable bundles
Jiaxuan Fan, Zhiyao Xiong, Xiaokui Yang +1
Let be a stable holomorphic vector bundle over a compact Kähler (or Gauduchon) manifold . We show that for any real number and any initial Hermitian metric …
The prescribed Hermitian-Yang-Mills flow II
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
We prove an analogue of the classical Donaldson-Uhlenbeck-Yau theorem by using the prescribed Hermitian-Yang-Mills flow. Let be a holomorphic vector bundle over a compact Kähle…
Existence of twisted Hermitian-Einstein metrics on unstable vector bundles
Mingwei Wang, Xiaokui Yang, Shing-Tung Yau
In this paper, we demonstrate that twisted Hermitian-Einstein metrics on holomorphic vector bundles exist without obstruction. More precisely, for an arbitrary holomorphic vector b…
The prescribed Hermitian-Yang-Mills flow I
Zhiyao Xiong, Xaokui Yang, Shing-Tung Yau
In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: where…
Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors I
Mingwei Wang, Xiaokui Yang, Shing-Tung Yau
In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem. Let be a holomorphic vector bundle over a compact Kähler manifold . Suppose that there e…