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A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
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Hajime Kawakami
Published/Copyright:
March 10, 2010
Abstract
We conjecture that the Gauss–Bonnet formula gives a necessary and sufficient condition for the existence of a metric deformation to obtain a positive/negative Gaussian curvature on a disk. The conjecture is reduced to a problem of a partial differential inequality with Dirichlet–Neumann boundary condition. We give a partial answer and an example.
Received: 2006-06-08
Published Online: 2010-03-10
Published in Print: 2008-March
© Heldermann Verlag
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Articles in the same Issue
- Functional Equations and μ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
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- On the 𝐿1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
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- Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
- On Some Properties of the Dirichlet Problem at Resonance
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- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers