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This is contained in Theorem 2.6 in chapter IV in the book of Barth, Peters, Van de Ven (in the new edition with Hulek, it is Theorem 2.7, chapter IV). It does not rely on classification, and it was …

I just found this paper by B. Datta (later published in J. Indian Math. Soc. 60 (1994), no. 1-4, 171–190) that explains in details why one key equation in Hsiung's paper is wrong. See the whole discus …

This is theorem 7.9 in the book of Kobayashi-Nomizu "Foundations of Differential Geometry Vol.II". There the authors attribute it to Hawley and Igusa independently. These are probably the first papers …

For what it's worth, the Navier-Stokes equation on manifolds is also mentioned in this recent paper http://arxiv.org/pdf/1107.2698, see (1.16) there, in connection with another flow for vector fields …

V.V. Shokurov has written several papers over the course of about 10 years which are called "Letters of a bi-rationalist". Here are the ones that I could find: Letters of a bi-rationalist. I. A proj …

As you hinted yourself, they were indeed discovered by W.V.D. Hodge. They appear explicitly in his 1941 book "The Theory and Applications of Harmonic Integrals", which you can find here, see e.g. the …

This is not literally the answer that the OP wanted (a reference to the literature, which I am not aware of), but following the comments above let me write down the simple gluing argument. Let $\wide …

This result follows from Corollaire (p.212) of this paper by F. Campana, Coréduction algébrique d'un espace analytique faiblement kählérien compact, Invent. Math. 63 (1981), no. 2, 187–223. I had the …

If I remember correctly, you can find this in the book "Complex Differential Geometry" by Fangyang Zheng in Chapter 7. The analogous result "with real coefficients" (i.e. for real vectors and with $S^ …

Kołodziej's and Klimek's books are very good, and Demailly's online book also has useful material. You can also try with Zbigniew Błocki's lecture notes http://gamma.im.uj.edu.pl/~blocki/publ/ln/wykl …

I think the book The shape of inner space by S.T. Yau with S. Nadis counts too, since more than half of it is an autobiography of Yau (and the other half discusses the implications of his research for …

My local library has the paper version, here is a scan.

The explicit polarization formula is the following, taken from this paper of Bishop and Goldberg. Working with real tangent vectors (instead of $(1,0)$ vectors, but it's easy to switch from one poin …

These manifolds have actually been studied to some extent by Campana and Peternell in their series of papers "Towards a Mori theory on compact Kähler threefolds I, II, III". In those papers they menti …

Does anyone have a copy of the unpublished preprint of Karen Uhlenbeck A priori estimates for Yang-Mills fields from around 1986? It appears to have circulated for some time, and it is quoted in seve …