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mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain...

mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R , {\displaystyle...

Sampson initiated the study of harmonic map heat flow, using a convergence theorem for the flow to show that any smooth map from a closed manifold to a closed...

geometry of energy-minimizing harmonic maps. Later, Mikhael Gromov had the insight that an extension of the theory of harmonic maps, to allow values in metric...

Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency...

Trivially, the coordinate system is harmonic if and only if, as a map U → ℝn, the coordinates are a harmonic map. A direct computation with the local...

In mathematics, a harmonic morphism is a (smooth) map ϕ : ( M m , g ) → ( N n , h ) {\displaystyle \phi :(M^{m},g)\to (N^{n},h)} between Riemannian manifolds...

Joseph Sampson on harmonic maps, various rigidity phenomena had been deduced from the combination of an existence theorem for harmonic mappings together...

1983. The study of harmonic maps, of which the study of biharmonic maps is an outgrowth (any harmonic map is also a biharmonic map), had been (and remains)...

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually...

differential geometry — the Bochner identity is an identity concerning harmonic maps between Riemannian manifolds. The identity is named after the American...

variational arguments can still be used to give general existence results" for harmonic map equations. Building on these ideas, Uhlenbeck initiated a systematic...

Holomorphic separability Meromorphic function Quadrature domains Harmonic maps Harmonic morphisms Wirtinger derivatives Analytic functions of one complex...

This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree ℓ = 10 {\displaystyle \ell =10} . Some of these...

conjecture. The analogous problem for harmonic maps, as opposed to Ding and Tian's consideration of the harmonic map flow, was considered by Changyou Wang...

arising in stochastic optimal control theory, and to the theory of harmonic maps. He is also well known as the author of the textbook Partial Differential...

principle for harmonic functions is that there are no compact complete minimal surfaces in R 3 {\displaystyle \mathbb {R} ^{3}} . Gauss map definition:...

a unique harmonic function u : D → Ω such that u = μ on ∂D and u is a diffeomorphism. R. Schoen, S. T. Yau. (1997) Lectures on Harmonic Maps. International...

mathematical analysis, geometry and topology, especially his work about harmonic maps in collaboration with James Eells. He obtained his Ph.D. in mathematics...