کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896617 | 1630590 | 2018 | 36 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On a combinatorial curvature for surfaces with inversive distance circle packing metrics
ترجمه فارسی عنوان
در انحنای ترکیبی برای سطوح با معیارهای بسته بندی دایره معکوس
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
In this paper, we introduce a new combinatorial curvature on triangulated surfaces with inversive distance circle packing metrics. Then we prove that this combinatorial curvature has global rigidity. To study the Yamabe problem of the new curvature, we introduce a combinatorial Ricci flow, along which the curvature evolves almost in the same way as that of scalar curvature along the surface Ricci flow obtained by Hamilton [20]. Then we study the long time behavior of the combinatorial Ricci flow and obtain that the existence of a constant curvature metric is equivalent to the convergence of the flow on triangulated surfaces with nonpositive Euler number. We further generalize the combinatorial curvature to α-curvature and prove that it is also globally rigid, which is in fact a generalized Bowers-Stephenson conjecture [6]. We also use the combinatorial Ricci flow to study the corresponding α-Yamabe problem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 3, 1 August 2018, Pages 523-558
Journal: Journal of Functional Analysis - Volume 275, Issue 3, 1 August 2018, Pages 523-558
نویسندگان
Huabin Ge, Xu Xu,