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$$L^p$$ -Đồng sinh, nhóm bán nhóm nhiệt và không gian phân lớp
Tóm tắt
Giả sử (M, g) là một đa tạp Riemann chưa đầy đủ có thể tích hữu hạn và $$2\le p<\infty $$. Trong phần đầu tiên của bài báo này, chúng tôi chứng minh rằng dưới một số giả thiết nhất định, việc bao hàm không gian của các dạng vi phân $$L^p$$ vào không gian của các dạng vi phân $$L^2$$ sẽ dẫn đến một ánh xạ tiêm/biến hình giữa các nhóm đồng sinh $$L^p$$ và $$L^2$$ tương ứng. Sau đó, ở phần thứ hai, chúng tôi cung cấp nhiều ứng dụng của những kết quả này cho độ cong và đồng sinh giao của các pseudomanifold phân lớp Thom–Mather compact và các biến thể dự án phức tạp chỉ có các điểm kỳ dị đơn lẻ.
Từ khóa
#Đồng sinh #Dạng vi phân #Đa tạp Riemann #Độ cong #Pseudomanifold #Biến thể dự án phức tạpTài liệu tham khảo
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