Long-term MODIS vegetation index records were used to extract regularly-repeating seasonal and interannual greenness cycles in Hawaiian ecosystems using harmonic analysis. With two vegetation indices, NDVI and EVI, the MODIS system provided an opportunity to combine the two measures and create a hybrid approach to the leaf phenology study in a diversity of Hawaiian ecosystems. Despite data nois...

sectionHarmonic Volumetric Parameterization using MFS After the decomposition of a given object M , we get a set of star shapes {Mi}, each region being guarded by a point gi. Then we can parameterize each subregion onto a solid sphere. A key property that we will show shortly is that such a harmonic map is guaranteed to be bijective. The harmonic map can be computed using the method of fundamen...

We prove that the standard half-harmonic map U : R → S defined by x → ( x−1 x2+1 −2x x2+1 ) is nondegenerate in the sense that all bounded solutions of the linearized half-harmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation and rotation) of U .

In this paper, we construct a new type of singularity which may occur in weak solutions of the harmonic map flow for two-dimensional domains. This " reverse bubbling " singu-larity may occur spontaneously, and enables us to construct solutions to the harmonic map heat equation which differ from the standard Struwe solution, despite agreeing for an arbitrarily long initial time interval.

Hodge theory is a fundamental tool of Kähler geometry. It represents cohomology classes by harmonic forms, and deriving properties of these harmonic forms then in turn yields information about the cohomology. Homology or cohomology groups, however, contain only partial information about the topology of a manifold. The most important topological invariant of a manifold X is the fundamental group...

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

Harmonic morphism is a smooth map between Riemannian manifolds which pulls back germs of harmonic functions to germs of harmonic functions. It may be charactrized as harmonic maps which are horizontally weakly conformal [5,9]. One task of studying harmonic morphism is constructing concrete examples; Another one is classification of all harmonic morphisms between all special manifolds (in partic...

Let Σ be a compact Riemann surface. Any sequence fn : Σ —> M of harmonic maps with bounded energy has a "bubble tree limit" consisting of a harmonic map /o : Σ -> M and a tree of bubbles fk : S 2 -> M. We give a precise construction of this bubble tree and show that the limit preserves energy and homotopy class, and that the images of the fn converge pointwise. We then give explicit counterexam...

Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ : M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and ...