Về sự tồn tại của các lặp thể $$C^{1,1}$$-isometric của nhiều lớp bề mặt cong âm vào $$\mathbb {R}^3$$

Archive for Rational Mechanics and Analysis - Tập 236 - Trang 419-449 - 2019
Siran Li1,2
1Department of Mathematics, Rice University, Houston, USA
2Department of Mathematics, McGill University, Montreal, Canada

Tóm tắt

Chúng tôi chứng minh sự tồn tại của các lặp thể $$C^{1,1}$$-isometric của nhiều lớp bề mặt Riemann cong âm $$({\mathcal {M}},g)$$ vào không gian Euclid 3 chiều $$\mathbb {R}^3$$, bao gồm mặt phẳng siêu phẳng chuẩn, các metric kiểu xoắn tổng quát, và các metric Enneper tổng quát. Chứng minh của chúng tôi dựa trên lý thuyết về sự nén bù và phương pháp khu vực bất biến trong các định luật bảo toàn hyperbolic, cùng với một số quan sát mới về các đại lượng hình học liên quan (độ cong Gauss, các thành phần metric, v.v.) cho các bề mặt cong âm.

Từ khóa

#Bề mặt Riemann #cong âm #lặp thể isometric #lý thuyết nén bù #độ cong Gauss

Tài liệu tham khảo

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