Volume 55

2018

Publication date: 30.11.2018

Licence: CC BY-NC-ND

Editorial team

Editor-in-Chief Sławomir Kołodziej

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Systems of holomorphic multivalued projections on complex manifolds

Kamil Drzyzga

Universitatis Iagellonicae Acta Mathematica, Volume 55, 2018, pp. 7-19

https://doi.org/10.4467/20843828AM.18.001.9717

Let M be a submanifold of a connected Stein manifold X . We construct a global system of holomorphic multivalued projections X −→M . In particular, for every locally bounded family F ⊂ O(M ) we get a continuous extension operator F −→ O(X ).

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Measure Estimates, Harnack Inequalities and Ricci Lower Bound

Yu Wang, Xiangwen Zhang

Universitatis Iagellonicae Acta Mathematica, Volume 55, 2018, pp. 21-51

https://doi.org/10.4467/20843828AM.18.002.9718

On the Riemannian metric-measure space, we establish an Alexandrov–Bakelman–Pucci type estimate connecting the Bakry–E´ mery Ricci curvature lower bound, the modified Laplacian and the measure of certain special sets. We apply this estimate to prove the Harnack inequalities for the modified Laplacian operator (and fully non-linear operators, see the Appendix). These inequalities seem not available in the literature and our proof, based solely on the ABP estimate, does not use standard techniques.

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Movable intersection and bigness criterion

Jian Xiao

Universitatis Iagellonicae Acta Mathematica, Volume 55, 2018, pp. 53-64

https://doi.org/10.4467/20843828AM.18.003.9719

In this note, we give a Morse-type bigness criterion for the difference of two pseudo-effective (1, 1)-classes by using movable intersections. As an application, we give a Morse-type bigness criterion for the difference of two movable (n − 1, n − 1)-classes.

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Słowa kluczowe: Multivalued projections, holomorphic continuation, ABP estimate, Krylov–Safonov Harnack inequality, metric- measure space, Bakry–Emery Ricci curvature, weighted Laplacian operator, Pucci operator, Kahler manifolds, line bundles, Morse inequalities, currents

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