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In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.
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참고문헌 (14)
참고문헌 신청
Huai-Dong Cao / 2014 / Bach-flat gradient steady Ricci solitons / Calculus of Variations and Partial Differential Equations 49(1-2):125~138
Huai-Dong Cao / 2020 / Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons / The Journal of Geometric Analysis 30(1):511~525
Huai-Dong Cao / 2006 / A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow / Asian Journal of Mathematics 10(2):165~492
Giovanni Catino / 2016 / Classification of expanding and steady Ricci solitons with integral curvature decay / Geometry & Topology 20(5):2665~2685
G. Catino / 2017 / Gradient Ricci solitons with vanishing conditions on Weyl / J. Math. Pures Appl 108(1):1~13
Huai-Dong Cao / 2020 / Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons / The Journal of Geometric Analysis 30(1):511~525
Huai-Dong Cao / 2006 / A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow / Asian Journal of Mathematics 10(2):165~492
Giovanni Catino / 2016 / Classification of expanding and steady Ricci solitons with integral curvature decay / Geometry & Topology 20(5):2665~2685
G. Catino / 2017 / Gradient Ricci solitons with vanishing conditions on Weyl / J. Math. Pures Appl 108(1):1~13
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