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Hajime Uraka
STABILITY OF HARMONIC MAPS AND EIGENV ALVES OF THE LAPLACIAN
A. Lichnerowicz (1958)
Géométrie des groupes de transformations
S Seto, G Wei (2017)
First eigenvalue of the $$p$$ p -Laplacian under integral curvature conditionNonlinear Anal., 163
YM Shi, HC Zhang (2007)
Lower bounds for the first eigenvalue on compact manifoldsChin. Ann. Math. Ser. A, 28
J. Zhong, Hongcang Yang (1984)
ON THE ESTIMATE OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLDScience in China Series A-Mathematics, Physics, Astronomy & Technological Science, 27
S. Seto, G. Wei (2017)
First eigenvalue of the $p$-Laplacian under integral curvature condition
E. Aubry (2007)
Finiteness of π1 and geometric inequalities in almost positive Ricci curvatureAnnales Scientifiques De L Ecole Normale Superieure, 40
G. Carron (2016)
Geometric inequalities for manifolds with Ricci curvature in the Kato classarXiv: Differential Geometry
Hung-hsi Wu (1991)
The Estimate of the First Eigenvalue of a Compact Riemannian Manifold
Peter Li (2012)
Geometric Analysis: Mean value constant, Liouville property, and minimal submanifolds
Shi Yumin (2007)
Lower Bounds for the First Eigenvalue on Compact ManifoldsChinese Annals of Mathematics
Xavier Oliv'e (2017)
Neumann Li-Yau gradient estimate under integral Ricci curvature boundsarXiv: Differential Geometry
Yuntao Zhang, Kui Wang (2016)
An alternative proof of lower bounds for the first eigenvalue on manifoldsMathematische Nachrichten, 290
P. Petersen, G. Wei (1997)
Relative Volume Comparison with Integral Curvature BoundsGeometric & Functional Analysis GAFA, 7
G. Wei, R. Ye (2007)
A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian ManifoldsJournal of Geometric Analysis, 19
Christian Rose (2016)
Li–Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato classAnnals of Global Analysis and Geometry, 55
B. Andrews, Lei Ni (2011)
Eigenvalue Comparison on Bakry-Emery ManifoldsCommunications in Partial Differential Equations, 37
B. Andrews, J. Clutterbuck (2012)
Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalueAnalysis & PDE, 6
(2012)
GeometricAnalysis, Cambridge Studies inAdvancedMathematics, vol
Qi Zhang, Meng Zhu (2016)
Li-Yau gradient bound for collapsing manifolds under integral curvature conditionarXiv: Differential Geometry
(2005)
Curvature-up through the twentieth century, and into the future? [translation of Sūgaku 54(3), 292–307 (2002)
Piotr lasz (2014)
GEOMETRIC ANALYSIS
Jeff Cheeger (2015)
Problems in Analysis: A Symposium in Honor of Salomon Bochner (PMS-31)
Qi Zhang, Meng Zhu (2015)
Li–Yau gradient bounds on compact manifolds under nearly optimal curvature conditionsJournal of Functional Analysis
Qing Han, F. Lin (2000)
Elliptic Partial Differential Equations
Q Han, F Lin (2011)
Elliptic Partial Differential Equations, Courant Lecture Notes
X. Dai, G. Wei, Zhenlei Zhang (2016)
Local Sobolev Constant Estimate for Integral Ricci Curvature BoundsarXiv: Differential Geometry
Casey Blacker, S. Seto (2018)
First eigenvalue of the $p$-Laplacian on Kähler manifoldsProceedings of the American Mathematical Society
M. Obata (1962)
Certain conditions for a Riemannian manifold to be isometric with a sphereJournal of The Mathematical Society of Japan, 14
D. Bakry, Z. Qian (2000)
Some New Results on Eigenvectors via Dimension, Diameter, and Ricci Curvature☆Advances in Mathematics, 155
Fengbo Hang, Xiaodong Wang (2010)
A remark on Zhong-Yang's eigenvalue estimateInternational Mathematics Research Notices, 2007
J. Cheeger (1969)
A lower bound for the smallest eigenvalue of the Laplacian
H. Yang (1990)
ESTIMATES OF THE FIRST EIGENVALUE FOR A COMPACT RIEMANN MANIFOLD
P. Kröger (1992)
On the spectral gap for compact manifoldsJournal of Differential Geometry, 36
S. Gallot (1988)
Isoperimetric inequalities based on integral norms of Ricci curvature
C Blacker, S Seto (2019)
First eigenvalue of the $$p$$ p -Laplacian on Kähler manifoldsProc. Am. Math. Soc., 147
Mu-Fa Chen, Feng-Yu Wang (1997)
General formula for lower bound of the first eigenvalue on Riemannian manifoldsScience in China Series A: Mathematics, 40
E Aubry (2007)
Finiteness of $$\pi _1$$ π 1 and geometric inequalities in almost positive Ricci curvatureAnn. Sci. École Norm. Sup. (4), 40
Peter Li, S. Yau (1980)
Estimates of eigenvalues of a compact Riemannian manifold
P. Petersen, C. Sprouse (1998)
Integral curvature bounds, distance estimates and applicationsJournal of Differential Geometry, 50
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We prove a sharp Zhong–Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature. Keywords Laplace eigenvalue · Integral Ricci curvature · Integral curvature · Eigenvalue estimate · Laplacian 1 Introduction One trend in Riemannian geometry since the 1950’s has been the study of how curvature affects global quantities like the eigenvalues of the Laplacian. On a closed Riemannian manifold (M , g), assuming that Ric ≥ (n − 1)H (H > 0), Lichnerowicz [16] proved the lower bound λ (M ) ≥ Hn,where λ is the first nonzero eigenvalue of the Laplace–Beltrami 1 1 operator in (M , g), div(∇u) := u =−λ u. G.W. is partially supported by NSF DMS 1811558. Q.S.Z. is partially supported by Simons Foundation Grant 282153. B Guofang Wei wei@math.ucsb.edu Xavier Ramos Olivé xramosolive@wpi.edu Shoo Seto shoos@uci.edu Qi S. Zhang qizhang@math.ucr.edu Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA Department of Mathematics, University of California, Irvine, CA 92617, USA Department of Mathematics, University of California, Santa Barbara, CA 93106, USA Department of Mathematics, University of California, Riverside, CA 92521, USA 123 X. Ramos Olivé et al. Obata [17] proved the rigidity result that equality holds
Mathematische Zeitschrift – Springer Journals
Published: Dec 5, 2019
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