Nonrigidity of compact elliptic embeddings and complete surfaces of finite area

This paper constructs counterexamples to both rigidity questions in Problem 55. The first is a real analytic family of pairwise noncongruent elliptic isometric embeddings of one closed 22-dimensional Riemannian manifold into 43-dimensional Euclidean space. The second is a smooth complete surface of finite area with Gaussian curvature satisfying −C ≤ K ≤ 0 for some finite constant C. This surface admits two isometric embeddings into three-dimensional Euclidean space with noncongruent images. Repository: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometryPDF at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/problem_55.pdfTeX source at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/yau_problem_55.tex