Canonical metrics on holomorphic bundles over compact bi-Hermitian manifolds

Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold

“…By employing a similar argument as presented in ( [1], Lemma 19) and ( [36], Lemma 3.3), it is straightforward to prove the subsequent lemma. Lemma 2.…”

“…If ε > 0, the implication in Proposition 7, stated in ( 14), leads to (19). According to the definition, it is straightforward to verify that…”

“…Drawing from Equation (36) and implementing the method outlined in ([4], Lemma 5.5), we deduce that for every v ∈ Q 0 , the eigenvalues of u ∞,v remain constant across almost all points. Denote the distinct eigenvalues of u ∞,v as µ 1,v < µ 2,v < • • • < µ l,v .…”

“…Research into the DUY theorem gained momentum in the 1980s, driven by numerous eminent mathematicians, as documented in works such as [1][2][3][4][5]. Over the past two decades, this theorem has continuously piqued the interest of numerous researchers, as evidenced by various publications ( [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references within). On 9 September 2021, Mochizuki was awarded the Breakthrough Prize in Mathematics for his remarkable contributions to the field of twistor D-modules.…”