naa a22 4500 510810438 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9239-3 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9239-3 Sung Chanyoung Dept. of Mathematics and Institute for Mathematical Sciences, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul, Korea aut Liouville-Type Theorems and Applications to Geometry on Complete Riemannian Manifolds [Elektronische Daten] [Chanyoung Sung] On a complete Riemannian manifold M with Ricci curvature satisfying $$\mathrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2\cdots (\log^{k}r)^2$$ for r≫1, where A>0 is a constant, and r is the distance from an arbitrarily fixed point inM, we prove some Liouville-type theorems for a C 2 function f:M→ℝ satisfying Δf≥F(f) for a function F:ℝ→ℝ. As an application, we obtain a C 0 estimate of a spinor satisfying the Seiberg-Witten equations on such a manifold of dimension4. We also give applications to the conformal transformation of the scalar curvature and isometric immersions of such a manifold. Mathematica Josephina, Inc., 2011 Subharmonic function nationallicence Liouville theorem nationallicence Seiberg-Witten equations nationallicence Scalar curvature nationallicence Isometric immersion nationallicence Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 96-105 1050-6926 23:1<96 2013 23 12220 https://doi.org/10.1007/s12220-011-9239-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9239-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sung Chanyoung Dept. of Mathematics and Institute for Mathematical Sciences, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul, Korea aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 96-105 1050-6926 23:1<96 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer