arXiv subjects

Sai Rasmi Ranjan Mohanty

Publications and source records attributed to Sai Rasmi Ranjan Mohanty.

4 recordsLinked to original sources

arXiv2026

Spectral and Logarithmic Atiyah Classes for Higgs Bundles

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 of the spectral line bundle and takes values in the centralizer of the Higgs field. Further, when the discriminant is reduced, we construct a logarithmic refinement across the branch divisor: the Atiyah class extends as a class with logarithmic poles and values in a natural regularized centralizer sheaf.

math.AG↗

arXiv2026

Duality of zero mean curvature surfaces in the Lorentzian Heisenberg group

We study a transformation surface associated with a zero mean curvature surface in the three-dimensional Heisenberg group with respect to two left-invariant semi-Riemannian metrics. We investigate the duality and prove that the transformation surface also has zero mean curvature. Furthermore, we derive the Sym formula for the dual surface in both metric cases.

math.DG↗

arXiv2024

Singularities on maxfaces constructed by node-opening

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 compact set and have arbitrarily many catenoid or planar ends, thus removing the scarcity of examples of maxfaces. The surfaces look like spacelike planes connected by small necks. Among the examples are maxfaces of the Costa--Hoffman--Meeks type. Although very fruitful, the main challenge of this paper is not the construction itself, but the analysis of the positions and natures of singularities on these maxfaces. More specifically, we conclude that the singular set form curves around the waists of the necks. In generic and some symmetric cases, all but finitely many singularities are cuspidal edges, and the non-cuspidal singularities are swallowtails evenly distributed along the singular curves.

math.DG↗

arXiv2022

Approximating singularities by a cuspidal edge on a maxface

We give necessary and sufficient conditions on the singular Björling data to the singular Björling problem's solution has a prescribed nature of singularity. As an application, we prove that near a maxface with a particular type of singularity, there is another maxface having a cuspidal-edge. An example of a maxface having various types of singularities is also given.

math.DG↗