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Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
$D_N$ type quantum Calogero model through free harmonic oscillators
2011/3/3
We solve the eigenvalue problem of the DN type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation.In particular, we construct the ei...
A general comparison theorem for $p$-harmonic maps in homotopy class
comparison theorem homotopy class
2010/11/22
We prove a general comparison result for homotopic finite $p$-energy $C^{1}$ $p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$ is $p$-parabolic and $N$ is complete and non...
An extremal decomposition problem for harmonic measure
An extremal decomposition problem harmonic measure
2010/11/23
Let $E$ be a continuum in the closed unit disk $|z|\le 1$ of the complex $z$-plane which divides the open disk $|z| < 1$ into $n\ge 2$ pairwise non-intersecting simply connected domains $D_k,$ such t...
We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends to zero. As an appli...
Eigenvalues and entropys under the harmonic-Ricci flow
Eigenvalues entropys the harmonic-Ricci flow
2010/11/12
In this paper, the author discuss the eigenvalues and entropys under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for c...
Regularity for $p$-Harmonic Systems with Gradient Below the Critical Growth
controllable growth p-harmonic systems full regularity
2007/12/11
In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, H\"older continuity spaces with any H\"older exponent ...