An -isolation theorem for Yang-Mills fields
Min-Oo (1982)
Compositio Mathematica
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Min-Oo (1982)
Compositio Mathematica
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A. Comtet (1980)
Annales de l'I.H.P. Physique théorique
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Walter Seaman (1986)
Annales de l'institut Fourier
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We prove that if the sectional curvature, , of a compact 6-manifold without boundary satisfies then its third (real) Betti number is zero.
Shigeru Kodani (1990)
Compositio Mathematica
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Mahta Khosravi, John A. Toth (2005)
Annales de l'institut Fourier
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Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case. ...
Dominique Bakry, Zhongmin M. Qian (1999)
Revista Matemática Iberoamericana
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Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.