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shupp_01

### Oberseminar Differentialgeometrie: Shih-Kai Chiu (Notre Dame), Vortrag: A Liouville type theorem for harmonic 1-forms

##### Montag, 06.07.2020 16:15 im Raum Zoom

Zoom-Meeting: https://wwu.zoom.us/j/97461739978 Abstract: The famous Cheng-Yau gradient estimate implies that on a complete Riemannian manifold with nonnegative Ricci curvature, any harmonic function that grows sublinearly must be a constant. This is the same as saying the function is closed as a 0-form. We prove an analogous result for harmonic 1-forms. Namely, on a complete Ricci-flat manifold with Euclidean volume growth, any harmonic 1-form with polynomial sublinear growth must be the differential of a harmonic function. We prove this by proving an L^2 version of the "gradient estimate" for harmonic 1-forms. As a corollary, we show that when the manifold is Ricci-flat Kähler with Euclidean volume growth, then any subquadratic harmonic function must be pluriharmonic.

Angelegt am Donnerstag, 04.06.2020 14:53 von shupp_01
Geändert am Donnerstag, 04.06.2020 14:53 von shupp_01
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