Would appreciate if someone could summarize the thread here, since tweets after the first are not visible if you don't have an account.

Linked paper from the x thread: https://arxiv.org/pdf/2411.19826

I had ChatGPT summarize this paper for me.

It's pretty impressive to me that a single post doc has this much breadth in a single paper.

Convex Geometry

  - Brunn-Minkowski theory
  - Surface Area Measure

Measure Theory

  - Lebesgue–Stieltjes Measure
  - Green’s Theorem

Differential Geometry

  - Weak derivatives for boundaries
  - Trajectories and rotation paths

Optimization and Functional Analysis

  - Quadratic functionals
  - Concavity and global optimization

Combinatorial Geometry

  - Balanced polygons
  - Iterative approximation and discretization

Computational Geometry

  - Numerical simulations
  - Verification of bounds and injectivity

Advanced Theorems

  - Mamikon’s Theorem
  - Jordan Curve Theorem

I think it would probably take me 50 years just to fully comprehend this proof alone. Amazing work.