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On the Discrete Differential Geometry of Surfaces in S4
integrable klein lie quaternion touch
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2014/12/8
The Grassmannian space GC(2, 4) embedded in CP5 as the Klein quadric of twistor theory has a natural interpretation in terms of the geometry of “round” 2-spheres in S4. The incidence of two lines in C...
AQUIFER GEOMETRY, BASEMENT-TOPOGRAPHY AND GROUND WATER QUALITY AROUND KEN GRABEN, INDIA
DEM Basement topography Remote Sensing GIS Aquifer geometry
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2014/11/12
In this study a systematic approach has been made for the analysis of Ken graben area by
integrating the remote sensing data with the hydrologic data to study the subsurface
geological and geomorph...
Boundary Element Method Numerical Modeling: An Approach for Analyzing the Complex Geometry and Evolution of the San Gorgonio Knot, San Andreas Fault, Southern California
Boundary Element Method Numerical Modeling Complex Geometry Evolution of the San Gorgonio Knot San Andreas Fault Southern California
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2014/10/22
The San Andreas fault forms the right lateral transform boundary between the North American and Pacific tectonic plates. At various locations along the San Andreas fault the geometry of the fault surf...
A REMARK ON GEODESIC GEOMETRY OF TEICHMULLER SPACES
GEODESIC GEOMETRY TEICHMULLER SPACES
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2014/9/26
Let T (S) be the Teichm¨uller space of a hyperbolic Riemann surface S and let
Belt(S) be the Banach space of bounded measurable Beltrami differentials μ =
μdz/dz on S with L∞-norms. Suppose M(...
A class of variational functionals in conformal geometry
A class of variational functionals in conformal geometry
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2014/4/3
We derive a class of variational functionals which arise naturally in
conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides wi...
On a fully non-linear elliptic PDE in conformal geometry
Fully nonlinear PDE generalized Yamabe problem
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2014/4/3
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
FOURTH ORDER EQUATIONS IN CONFORMAL GEOMETRY
FOURTH ORDER EQUATIONS CONFORMAL GEOMETRY
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2014/4/3
In this artile we review some reent work on fourth order equations in onformal geometry of three and four dimensions. We dis uss some an existene result for a Yamabe-type equation in dimension three. ...
Fractional Laplacian in conformal geometry
Conformal geometry Fractional Laplacian Conformally covariant operators Dirichlet-to-Neumann operators Asymptotically hyperbolic manifolds
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2014/4/3
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal...
SOME PROGRESS IN CONFORMAL GEOMETRY
SOME PROGRESS CONFORMAL GEOMETRY
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2014/4/3
In this paper we describe our current research in the theory of partial di erential equations in conformal geometry. We introduce a bubble tree structure to study the degeneration of a class of Yamabe...
ON UNIQUENESS OF SOLUTION OF A n-TH ORDER DIFFERENTIAL EQUATION IN CONFORMAL GEOMETRY
ON UNIQUENESS OF SOLUTION A n-TH ORDER DIFFERENTIAL EQUATION CONFORMAL GEOMETRY
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2014/4/3
In this paper, we prove an uniqueness theorem for a n-th order elliptic equation on the standard n-sphere Sn. The problem arises naturally from the point of view of conformal geometry. The method we u...
Computational Conformal Geometry Applications
calculate Geometry Applications
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2014/10/30
The work is collaborated with Shing-Tung Yau, Feng Luo, Tony
Chan, Paul Thompson, Yalin Wang, Ronald Lok Ming Lui, Hong
Qin, Dimitris Samaras, Jie Gao, Arie Kaufman, and many other
mathematicians, ...
Einstein metrics in projective geometry
projective differential geometry Einstein metrics conformal differential geometry
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2012/7/11
It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined...
Fractals, coherent states and self-similarity induced noncommutative geometry
self-similarity fractals squeezed coherent states noncommutative geometry dissipation
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2012/6/30
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are relate...
Geometry of optimal control for control-affine systems
affine distributions optimal control theory Cartan's method of equivalence
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2012/6/21
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We comput...
Non-modal analysis of the diocotron instability. Plane geometry
Non-modal analysis the diocotron instability Plane geometry Plasma Physics
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2012/5/31
The comprehensive investigation of the temporal evolution of the diocotron instability of the plane electron strip on the linear stage of its development is performed. By using the Kelvin's method of ...