We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation. The method is mainly the Moser iteration technique which has been used and developed by \cite{BKN89}, \cite{Tian90}, \cite{TV05a} and others…
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7 results for “harmonic-Einstein”
The paper examines properties of generalized τ-quasi Ricci-harmonic metrics and proves rigidity results.
problem Characterizing and proving rigidity of generalized τ-quasi Ricci-harmonic metrics.
method Exploring conditions for harmonic-Einstein metrics, obtaining rigidity results, and proving gap theorems.
result Rigidity results for compact generalized τ-quasi Ricci-harmonic metrics.
Study expanding Ricci solitons on vector bundles, reducing to Higgs bundle equations.
problem Understanding the long-time behavior of Ricci flows on manifolds.
method Prove equations dimension-reduce to twisted harmonic-Einstein equations, establish correspondence with G-Higgs bundles.
result Produce infinite families of new non-locally homogeneous examples, complete description in dimension 4.
In the present paper, by using estimates for the generalized Ricci curvature, we shall give some gap theorems for Ricci-harmonic solitons showing some necessary and sufficient conditions for the solitons to be harmonic-Einstein. Our results may be regarded as a generalization of recent works by H. Li, and M. Fernandez-…
Extends Eells-Sampson theorem for manifolds with positive sectional curvature bounds.
problem Rigidity of harmonic maps between manifolds with curvature constraints.
method Proves an extension of Eells-Sampson theorem under positive sectional curvature upper bounds.
result Recover Hamilton's rigidity result for positive Ricci curvature.
The paper explores harmonic and asymptotically harmonic Finsler manifolds and their properties.
problem Characterizing and understanding harmonic Finsler manifolds.
method Investigation of various types of harmonic Finsler manifolds, characterizations via mean curvature and Laplacian, and construction techniques.
result Certain harmonic Finsler manifolds are of Einstein type and examples of non-Riemannian Finsler harmonic manifolds are provided.
The paper generalizes Bach and Einstein equations with a field.
problem Generalizing classical equations in presence of a field.
method Introducing and characterizing new tensors and manifolds.
result Variational characterization of new flat and harmonic-Einstein manifolds.