6 papers
Critical-point-free energy for fractional-Toledo representations
Rivu Bardhan, Anu Dhochak, Pradip Kumar
Let be a closed oriented surface of genus . For a reductive representation $ρ:π_1(S_g)\to\PU(2,1)$, let be the energy function on Teichmüller space associated to…
Spectral and Logarithmic Atiyah Classes for Higgs Bundles
Pradip Kumar, Sai Rasmi Ranjan Mohanty, Savita Rani +1
For a regular semisimple Higgs bundle with a smooth spectral curve, we prove that, over the \etale\ locus, the Atiyah class of the underlying bundle is induced by the Atiyah class…
Two characters on one punctured Riemann surface
Pradip Kumar
We develop an abstract framework for coupled period--realization of meromorphic --forms on punctured Riemann surfaces. A configuration datum gives the combinatorics and dete…
Singularities on maxfaces constructed by node-opening
Hao Chen, Anu Dhochak, Pradip Kumar +1
The node-opening technique, originally designed for constructing minimal surfaces, is adapted to construct a rich variety of new maxfaces of high genus that are embedded outside a…
Cuspidal crosscaps and folded singularities on a maxface and a minface
Rivu Bardhan, Anu Dhochak, Pradip Kumar
For a given zero mean curvature surface (in the Lorentz Minkowski space) having folded singularity, we construct a family of maxface and minface, having increasing cuspidal cro…
Genus Zero Complete Maximal Maps and Maxfaces with an Arbitrary Number of Ends
Pradip Kumar, Sai Rashmi Ranjan Mohanty
We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions un…