Construction of arbitrary genus maxfaces in the Lorentz-Minkowski space

Speaker: Anu Dhochak

ICTS-TIFR, Bengaluru, India

About the Series

This talk discusses the construction of maximal surfaces (maxfaces) in Lorentz-Minkowski space with arbitrary genus, highlighting methods, geometric properties, and connections to minimal surface theory. Prerequisites: Basic differential geometry of curves and surfaces, familiarity with curvature and genus; some exposure to minimal surfaces is helpful.

Schedule

Introduction to minimal and maximal surfaces in $\mathbb{R}^3$ and $\mathbb{L}_1^3$ respectively

Part 1 of the series

Tuesday, April 14, 2026

04:00 PM IST

Abstract: In this talk, we will discuss minimal and maximal surfaces in three-dimensional Euclidean and Lorentz-Minkowski space respectively. We will explore how they are related and how to construct them. In particular, we will cover Björling problem and Weierstrass-Ennerper representations for them. I will also define the term maxface on which my next two lectures will be.

Post-Lecture Resources:

Watch Recording Lecture Notes

Talk Concluded

This talk has ended — see the recording.

Node-opening construction of maxfaces

Part 2 of the series

Tuesday, April 21, 2026

04:00 PM IST

Abstract: In this talk, we will discuss the existence of a 1-parameter family of arbitrary genus maxfaces with an arbitrary number of spacelike ends and infinitely many swallowtails. Our primary tool of construction will be node-opening technique. All maxfces of these families are embedded in a wider sense. We will also see families of Lorentzian Costa and Costa-Hoffman-Meeks surfaces, as well as periodic surfaces of infinite genus, as examples.

Post-Lecture Resources:

Watch Recording Lecture Notes

Talk Concluded

This talk has ended — see the recording.

About the Speaker

Anu Dhochak

ICTS-TIFR, Bengaluru, India

Anu Dhochak is a postdoctoral fellow at ICTS-TIFR, Bengaluru, working with Professor Rukmini Dey. Her broad area of research is Differential Geometry. Her interest lies in construction on minimal and maximal surfaces. Recently, she is also exploring non-abelian Hodge theory on Sasakian Manifolds and the study of non-zero constant mean curvature surfaces in $\mathbb{R}^3$.

Email: anu.dhochak@icts.res.in
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