Analysis

These are a collection of exercises in minimal surfaces, most of which are taken from “A Course in Minimal Surfaces” by Colding and Minicozzi. I am still adding to this document, so please feel free to contact me if you find any errors.

Detailed proof of the monotonicity formula for energy minimizing maps and a discussion of the density function and monotone quanities.

This is the outline for a talk delivered on Feburary 21st, 2025 at the Rutgers student operated Grad Analysis Seminar.

The following is a short presentation on Hardy Spaces for MATH507 - Functional Analysis with Professor Maxime Van de Moortel. The presentation includes a brief introduction to H^p spaces and a proof that H^p is a Banach space for all p from 1 to infinity.

The following exercises are an assortment of homework problems from MATH 502 - Theory of Functions of a Real Variable II with Professor Dennis Kriventsov at Rutgers University. Topics include Radon Measures, weak convergence, Haar measures, Fourier analysis, PDEs, distributions, and probability theory.