Shiv Parsad

activity

20142026

collaborators

9 papers

math.GT2026

Minima of geodesic length functions for non-uniform filling systems

Subash Chandra Behera, Shiv Parsad

Kerckhoff proved that the geodesic length function $ℓ_{Ω}$ of a filling $Ω$ on $S_{g}$ attains a unique minimum in Teichmüller space. Recent work of Ernesto Girondo et al. computed…

math.GT2025

Some analogues of isoperimetric inequality

Subash Chandra Behera, Shiv Parsad

The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric…

math.GT2025

Filling systems of maximum size

Rakesh Kumar, Shiv Parsad

Let $S_{g}$ be a closed orientable surface of genus $g \geq 2$ . A collection $Ω = {γ_{1}, \dots, γ_{s}}$ of pairwise non-homotopic simple closed curves on $S_{g}$ such that $γ_{i}$ and $γ_j…

math.GT2024

Angle Parametrization of Teichmüller space and hyperelliptic surfaces

Subash Chandra Behera, Shiv Parsad

Let $S_{g}$ be a closed orientable surface of genus $g \geq 2$ , and let $T_{g}$ be the Teichmüller space of $S_{g}$ . Let $H_{g}$ denotes the space of all hyperelliptic…

math.GT2018

Geometric realizations of cyclic actions on surfaces -- II

Atreyee Bhattacharya, Shiv Parsad, Kashyap Rajeevsarathy

Let $Mod (S_{g})$ denote the mapping class group of the closed orientable surface $S_{g}$ of genus $g \geq 2$ . Given a finite subgroup $H$ of $Mod (S_{g})$ , let $\mathrm{F…

math.GT2017

Filling systems on surfaces

Shiv Parsad, Bidyut Sanki

Let $F_{g}$ be a closed orientable surface of genus $g$ . A set $Ω = {γ_{1}, \dots, γ_{s}}$ of pairwise non-homotopic simple closed curves on $F_{g}$ is called a \emph{filling system} or…

math.GT2017

Conjugation Orbits of Loxodromic Pairs in SU(n,1)

Krishnendu Gongopadhyay, Shiv Parsad

Let $H_{C}^{n}$ be the $n$ -dimensional complex hyperbolic space and $SU (n, 1)$ be the (holomorphic) isometry group. An element $g$ in $SU (n, 1)$ is called lox…

math.GT2017

Geometric realizations of cyclic actions on surfaces

Shiv Parsad, Kashyap Rajeevsarathy, Bidyut Sanki

Let $Mod (S_{g})$ denote the mapping class group of the closed orientable surface $S_{g}$ of genus $g \geq 2$ , and let $f \in Mod (S_{g})$ be of finite order. We give an induc…

math.GT2014

On Fenchel-Nielsen Coordinates of Surface Group Representations into SU(3,1)

Krishnendu Gongopadhyay, Shiv Parsad

Let $Σ_{g}$ be a compact, connected, orientable surface of genus $g \geq 2$ . We ask for a parametrization of the discrete, faithful, totally loxodromic representations in the deforma…