caa a22 4500 445843438 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0350-2 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0350-2 On the prescribing σ 2 curvature equation on $${\mathbb S^4}$$ [Elektronische Daten] [Sun-Yung Chang, Zheng-Chao Han, Paul Yang] Prescribing σ k curvature equations are fully nonlinear generalizations of the prescribing Gaussian or scalar curvature equations. For a given a positive function K to be prescribed on the 4-dimensional round sphere, we obtain asymptotic profile analysis for potentially blowing up solutions to the σ 2 curvature equation with the given K; and rule out the possibility of blowing up solutions when K satisfies a non-degeneracy condition. Under the same non-degeneracy condition on K, we also prove uniform a priori estimates for solutions to a family of σ 2 curvature equations deforming K to a positive constant; and under an additional, natural degree condition on a finite dimensional map associated with K, we prove the existence of a solution to the σ 2 curvature equation with the given K using a degree argument involving fully nonlinear elliptic operators to the above deformation. Springer-Verlag, 2010 Chang Sun-Yung Department of Mathematics, Princeton University, 08540, Princeton, NJ, USA aut Han Zheng-Chao Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, 08854, Piscataway, NJ, USA aut Yang Paul Department of Mathematics, Princeton University, 08540, Princeton, NJ, USA aut Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 539-565 0944-2669 40:3-4<539 2011 40 526 https://doi.org/10.1007/s00526-010-0350-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0350-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chang Sun-Yung Department of Mathematics, Princeton University, 08540, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Han Zheng-Chao Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, 08854, Piscataway, NJ, USA aut NATIONALLICENCE 700 1- Yang Paul Department of Mathematics, Princeton University, 08540, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 539-565 0944-2669 40:3-4<539 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer