5 papers
Hyperbolic Completion of Newton's Off-Center Orbit Problem: Constant-Curvature Rigidity, Symmetry, and Magnetic Uniqueness
Dipesh Bhandari
The hyperbolic potential was identified by Olshanii as the negative-curvature counterpart of Newton's off-center circular-orbit problem. We first sh…
Biharmonic Conformal Immersions of Hypersurfaces: Dirac Rigidity and Mixed Clifford Geometry
Dipesh Bhandari
A biharmonic conformal immersion asks whether a hypersurface can become a critical point of the bienergy after a conformal change of the domain metric. We study when this flexibili…
Making Surfaces Biharmonic by Conformal Reparametrization in Anti-de Sitter Three-Space
Dipesh Bhandari
Harmonic immersions of surfaces are minimal, while biharmonic maps form a fourth-order extension of harmonic-map theory. Because every harmonic map is automatically biharmonic, the…
A Kac-Weyl Character Identity
Michael A. Baker, Dipesh Bhandari, Michael Crescimanno
An explicit quantization of Chern-Simons theory leads to an identity between sums of the Kac-Weyl characters. One can use this identity to prove inequalities that constrain the fus…
Newton's Off-Center Circular Orbits and the Magnetic Monopole
Dipesh Bhandari, Michael Crescimanno
Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the dynamical symmetry leads to a unique choice of field…