An efficient statistical algorithm of automatic extracting road from SAR images is devised in this paper. First, an feature detecting operator is used to find the road candidate. Then another smaller operator which calculating the homogenous statistic of locate region is applied to reduce the false alarm and smooth the road edge. Finally, the road linear features are extracted by fusing the res...

We construct noncompact solutions to the affine normal flow of hypersurfaces, and show that all ancient solutions must be either ellipsoids (shrinking solitons) or paraboloids (translating solitons). We also provide a new proof of the existence of a hyperbolic affine sphere asymptotic to the boundary of a convex cone containing no lines, which is originally due to Cheng-Yau. The main techniques...

For positive p-harmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension n, p and the radius of the ball on which the function is de…ned. Our approach is based on a careful application of the Moser iteration technique and is di¤erent from Cheng-Yau’s method [2] employed ...

The subject began in 1975, when Yau [Y1] proved that there are no nonconstant, positive harmonic functions on a complete manifold with nonnegative Ricci curvature. A few years later, Cheng [C] pointed out that using a local version of Yau’s gradient estimate, developed in his joint work with Yau [CY], one can show that there are no nonconstant harmonic functions of sublinear growth on a manifol...

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded ...

We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli spaces to simple moduli spaces. It is a key technique in the proof of the general mirror formula, the proof of the Hori-Vafa formula for explicit expressions...

with the infinite boundary value condition u = +∞ on ∂Ω. (1.2) We will look for strictly convex solutions in C∞(Ω); it is necessary to assume the underlying domain Ω to be convex for such solutions to exist. This problem was first considered by Cheng and Yau ([5], [6]) for ψ(x, u) = eKuf(x) in bounded convex domains and for ψ(u) = e2u in unbounded domains. More recently, Matero [11] treated the...

For a smooth strictly convex closed hypersurface Σ in R, the Gauss map n : Σ → S is a diffeomorphism. A fundamental question in classical differential geometry concerns how much one can recover through the inverse Gauss map when some information is prescribed on S ([27]). This question has attracted much attention for more than a hundred years. The most notable example is probably the Minkowski...

The Gopakumar–Vafa invariant is a number defined as certain linear combination of the Gromov–Witten invariants. We prove that the GV invariants of the toric Calabi–Yau threefold are integers and that the invariants at high genera vanish. The proof of the integrality is the elementary number theory and that of the vanishing uses the operator formalism and the exponential formula.

We study modular differential equations for the basic weak Jacobi forms in one abelian variable with applications to elliptic genus of Calabi--Yau varieties. show that any $CY_3$ satisfies a equation degree respect heat operator. For $K3$ surface or $CY_5$ is $3$. prove general $CY_4$ its $5$. give examples two operator similar Kaneko--Zagier variable. find type $2$ $3$ second, third and fourth...