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1.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

2.
Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with diseontinuous interface conditlons. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process: when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.  相似文献   

3.
Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give an lower bound on the life span of a smooth immersed solution, which depends only on how much the curvature of the initial surface is concentrated in space.  相似文献   

4.
We discuss a filtration problem in a bounded one-dimensional porous medium. Suppose that the.volumetric moisture content at the surface is constant, and the bottom is impermeable. We prove thatthe solution will tend uniformly to a stable solution of the filtration equation as time tends to infinity.An explicit expression of the limiting profile is given.  相似文献   

5.
Inequalities of Korn's type on a surface with boundary have been proved in many papers using different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn's type on a compact surface without boundary. The idea is to use a finite number of maps for defining the surface and the inequality of Korn's type without boundary conditions for every map and to recast these in a general functional analysis setting about quotient spaces.  相似文献   

6.
In this paper,the author explains the solutions of Sine-Gordon equation and KdVequation as the geodesic curvature of the leaves of a foliation on a surface of constantcurvature and negative constant curvature respectively.Therefore,a question which wasasked in a paper of S.S.Chern and K.Tenenblat is answered.  相似文献   

7.
The essential maximality of a Riemann surface of O_(AD)~0 is verified.Actually we haveproved something a little stronger,i.e.a modified Stoilow principle and its conversefor a functiou meromorphic on a non-compact subregion on a Riemann surface of O_(AD)~0.The significance of these assertions lies in that they fail to hold for the wider and morefamiliar class O_(AD).  相似文献   

8.
熊全治 《数学学报》1937,2(2):239-245
<正> 1.Introduction.Let the tangent surface of an analytic curve Cin ordinary space be cut by a plane through a tangent at an ordinarypoint O of C,then the plane section thus obtained has a point of in-flexion at O,provided that the plane is not osculating to C at O.Thisis a well-known fact.Prof.Bompiani has enriched the projectivedifferential geometry of a plane curve at the neighbourhood of a point ofinflexion by introducing various covariant osculants.Prof.Su hasgiven some remarkable properties of the loci of the cusp-tangent t ofthe seven-point cusped cubic of the plane section of the tangent surfacemade by a variable plane n through a tangent of C at O.Prof.Lanehas investigated the loci of the osculants and various points and linesintroduced by Prof.Bompiani.The object of this note is to obtain someproperties of other loci related to the same problem as considered byProf.Su.  相似文献   

9.
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using conformal mappings, one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition. By virtue of the Hilbert transform, the problem is equivalent to a quasilinear pseudodifferential equation for an almost ...  相似文献   

10.
The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient K of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of K.The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.  相似文献   

11.
In this paper, we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a Käahler-Einstein surface. We prove that the blow-up flow Σ s at a singular point (X 0, T 0) of a symplectic mean curvature flow Σ t or of a Lagrangian mean curvature flow Σ t is a nontrivial minimal surface in ?4, if Σ ?∞ is connected.  相似文献   

12.
Infinitesimal deformations of ribbed surfaces of revolution Sn with preservation of the normal curvature (A) or geodesic torsion (B) of the boundary parallel are investigated. The following are proved: a convex surface Sn is rigid under deformations (A) and (B); there are nonconvex surfaces Sn that are nonrigid under deformations (A) and (B); any surface Sn has second-order rigidity under deformations (A); a surface Sn that is nonrigid under these deformations.Translated from Mateniaticheskie Zametki, Vol. 10, No. 2, pp. 135–144, August, 1971.  相似文献   

13.
Consider on a complex 1-dimensional torus Tλ an abelian differential of the second kind αλ. Assign to each λ the period quotient of αλ for two independent cycles on Tλ. For appropriate choices of αλ, the image of the modular sphere under this map is simple to describe, extending the classical case of holomorphic αλ Using this information for different αλ simultaneously, we discuss applications to existence and uniqueness questions for the Chen-Gackstatter surface, the Costa surface, and the translation invariant periodic helicoid with handles. In particular, there is now a conceptual and essentially non-computational proof for the uniqueness of the Chen-Gackstatter surface.  相似文献   

14.
We classify the singularities of a surface ruled by conics: they are rational double points of type A n or D n . This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a “minimal way” from it.  相似文献   

15.
In this note we construct a 1-complex dimensional family of (marked) Schottky groups of genus 6 with the property that every closed Riemann surface of genus 6 admitting the group A5 as conformal group of automorphisms is uniformized by one of these Schottky groups. In the algebraic limit closure of this family we describe three noded Schottky groups uniformizing the three boundary points of the pencil described by González-Aguilera and Rodriguez. We are able to find a very particular Riemann surface of genus 6 which is a (local) extremal for a maximal set of homologically independent simple closed geodesics. We observe that it is not Wimann's curve, the only Riemann surface of genus 6 with S5 as group of conformal automorphisms. The Schottky uniformizations permit us to compute a reducible symplectic representation of A5.  相似文献   

16.
Diamond nucleation on the surface of C60 thin layers and intermediate layer of Si substrates are studied by scanning electron microscopy (SEM). The cross-section SEM images of diamond films show that diamond grains really nucleate on the surface of C60 thin layers. The SEM images of diamond nucleating sites show the nucleating aggregation of diamond on C60 surfaces. The preferential oriented diamond films are observed. The plasma pretreatment of C60 sublimating layers is a key factor for diamond nucleation.  相似文献   

17.
In this paper, we shall give a constructive characterization of triangulations on the nonorientable surface of genus 3 without K 6-minors. Our characterization implies that every 5-connected triangulation and every 4-representative triangulation on the surface has a K 6-minor.  相似文献   

18.
A JS surface is a minimal graph over a polygonal domain that becomes infinite in magnitude at the domain boundary. Jenkins and Serrin characterized the existence of these minimal graphs in terms of the signs of the boundary values and the side-lengths of the polygon. For a convex polygon, there can be essentially only one JS surface, but a non-convex domain may admit several distinct JS surfaces. We consider two families of JS surfaces corresponding to different boundary values, namely JS0 and JS1, over domains in the form of regular stars. We give parameterizations for these surfaces as lifts of harmonic maps, and observe that all previously constructed JS surfaces have been of type JS0. We give an example of a JS1 surface that is a new complete embedded minimal surface generalizing Scherk's doubly periodic surface, and show also that the JS0 surface over a regular convex 2n-gon is the limit of JS1 surfaces over non-convex stars. Finally we consider the construction of other JS surfaces over stars that belong neither to JS0 nor to JS1.  相似文献   

19.
A surface, generated by a one-parameter family of conics in projective 3-space, such that the tangent planes along a generating conic form a quadric cone, is called a surface of Blutel [1]. The surface is said to be of hyperbolic type, if the characteristic line of the plane of a generating conic intersects it in two different real points s1, s2. Formerly [5] it was shown that such a surface must be a quadric if it is unbranched along the curves, generated by s1, s2, these points not being stationary. In the present paper analogous results are established in the remaining cases when one or both points s1, s2 are fixed.

Herrn Prof. Dr. K. Strubecker zum 80. Geburtstag gewidmet  相似文献   

20.
In ℂn we consider an algebraic surface Y and a finite collection of hypersurfaces Si. Froissart’s theorem states that if Y and Si are in general position in the projective compactification of ℂn together with the hyperplane at infinity then for the homologies of Y \∪ Si we have a special decomposition in terms of the homology of Y and all possible intersections of Si in Y. We prove the validity of this homological decomposition on assuming a weaker condition: there exists a smooth toric compactification of ℂn in which Y and Si are in general position with all divisors at infinity. One of the key steps of the proof is the construction of an isotopy in Y leaving invariant all hypersurfaces Y ∩ Sk with the exception of one Y ∩ Si, which is shifted away from a given compact set. Moreover, we consider a purely toric version of the decomposition theorem, taking instead of an affine surface Y the complement of a surface in a compact toric variety to a collection of hypersurfaces in it.  相似文献   

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