DISCREPANCY OF A CONVEX SET WITH ZERO CURVATURE AT ONE POINT

摘要

Abstract > Let Ω be a convex body in <mat:math display="inline" altimg="urn:x-wiley:00255793:media:mtk12023:mtk12023-math-0001" wiley:location="equation/mtk12023-math-0001.png"> <mat:msup> <mat:mi mathvariant="double-struck">R</mat:mi> <mat:mi>d</mat:mi> </mat:msup> </mat:math> and assume that <mat:math display="inline" altimg="urn:x-wiley:00255793:media:mtk12023:mtk12023-math-0002" wiley:location="equation/mtk12023-math-0002.png"> <mat:mrow> <mat:mi>?</mat:mi> <mat:mi mathvariant="normal">Ω</mat:mi> </mat:mrow> </mat:math> is smooth with everywhere positive Gaussian curvature except for one flat point of order <mat:math display="inline" altimg="urn:x-wiley:00255793:media:mtk12023:mtk12023-math-0003" wiley:location="equation/mtk12023-math-0003.png"> <mat:mrow> <mat:mi>γ</mat:mi> <mat:mo>?</mat:mo> <mat:mn>2</mat:mn> </mat:mrow> </mat:math> . We consider the <mat:math display="inline" altimg="urn:x-wiley:00255793:media:mtk12023:mtk12023-math-0004" wiley:location="equation/mtk12023-math-0004.png"> <mat:msup> <mat:mi>L</mat:mi> <mat:mi>p</mat:mi> </mat:msup> </mat:math> norm of the discrepancy with respect to translations and rotations of a dilated copy of the set Ω. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > 让ω是凸起的 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00255793：MED：MTK12023：MTK12023-Math-0001”Wiley：Location =“等式/ MTK12023-Math-0001.png”> <mat：msup> <MAT：MI Mathvariant =“双击”> R </ MAT：MI> <MAT：MI> D </ MAT：MI> </ mat：msup> </ mat：math> 并假设 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00255793：MED：MTK12023：MTK12023-Math-0002”Wiley：Location =“等式/ MTK12023-Math-0002.png”> <MAT：MROW> <mat：mi>？</ mat：mi> <mat：mi mathvariant =“正常”>ω</ mat：mi> </ mat：MROW> </ mat：math> 除了一个平坦的订单外，无处不在的正极高斯曲率是光滑的 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00255793：Media：MTK12023：MTK12023-Math-0003”Wiley：Location =“等式/ MTK12023-Math-0003.png”> <MAT：MROW> <MAT：MI>γ</ MAT：MI> <mat：mo>？</ mat：mo> <MAT：MN> 2 </ MAT：MN> </ mat：MROW> </ mat：math> 。我们考虑这一点 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00255793：MED：MTK12023：MTK12023-Math-0004”Wiley：Location =“等式/ MTK12023-Math-0004.png”> <mat：msup> <MAT：MI> L </ MAT：MI> <MAT：MI> P </ MAT：MI> </ mat：msup> </ mat：math> 关于集合ω扩张副本的翻译和旋转的差异。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" > 著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-24593/'>《Mathematika: A Journal of Pure and Applied Mathematics 》</a> <b style="margin: 0 2px;">|</b><span>2020年第2期</span><b style="margin: 0 2px;">|</b> <span>共17页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li> <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span> <a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学 ;</a></span> </li> <li 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href="/patent-detail/06120190219.html">包括至少一个具有至少一个阻尼凸起的引导装置的记录和/或再现设备</a> <b>[P]</b> . <span> 中国专利： CN1180416C </span> <span> . 2004.12.15</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120104563181.html">包括至少一个具有至少一个阻尼凸起的引导装置的记录和/或再现设备</a> <b>[P]</b> . <span> 中国专利： CN1363093A </span> <span> . 2002-08-07</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130422512731.html">CONVEX OR CONCAVE SURFACE CURVATURE AMPLIFYING DEVICE AND CONVEX OR CONCAVE SURFACE CURVATURE DETECTING METHOD USING THE SAME</a> <b>[P]</b> . <span> 外国专利：  EP1697709B8 </span> <span> . 2012-03-28</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：凸或凹曲面曲率放大装置，以及使用相同的凸或凹曲面曲率检测方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130426798501.html">Motor vehicle reflector has partial retro reflective reflector element, and front surface that is provided with convex curvature in radius, where reflection section is provided with other convex curvature in other radius</a> <b>[P]</b> . <span> 外国专利：  DE102008056048A1 </span> <span> . 2010-05-06</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：机动车辆反射器具有部分后向反射反射器元件，并且前表面具有半径上的凸曲率，其中反射部分具有其他半径上的其他凸曲率。 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130445908058.html">Table has triangular top with two sides of same length and radius of curvature, one of which is convex and other concave, third side being convex and preferably also of same length and radius of curvature as other two</a> <b>[P]</b> . <span> 外国专利：  DE10023146A1 </span> <span> . 2001-11-15</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: 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