论文标题
在$ J $-Santaló的猜想上
On a $j$-Santaló Conjecture
论文作者
论文摘要
令$ k \ geq 2 $为整数。 In the spirit of Kolesnikov-Werner \cite{KW}, for each $j\in\{2,\ldots,k\}$, we conjecture a sharp Santaló type inequality (we call it $j$-Santaló conjecture) for many sets (or more generally for many functions), which we are able to confirm in some cases, including the case $j=k$ and the unconditional 案件。有趣的是，这个不平等家族的极端是$ l_j^n $ ball的元素。我们的结果还加强了\ cite {kw}的主要结果之一，该结果与情况相对应$ j = 2 $。我们猜想不平等的家族的所有成员都可以解释为经典的blaschke-santaló不平等现象的概括。相关的是，我们讨论了由K. Ball \ Cite {Ball-conjoxture}引起的猜想的类似物，并在多输入设置中建立了与$ J $-Santaló猜想的连接。
Let $k\geq 2$ be an integer. In the spirit of Kolesnikov-Werner \cite{KW}, for each $j\in\{2,\ldots,k\}$, we conjecture a sharp Santaló type inequality (we call it $j$-Santaló conjecture) for many sets (or more generally for many functions), which we are able to confirm in some cases, including the case $j=k$ and the unconditional case. Interestingly, the extremals of this family of inequalities are tuples of the $l_j^n$-ball. Our results also strengthen one of the main results in \cite{KW}, which corresponds to the case $j=2$. All members of the family of our conjectured inequalities can be interpreted as generalizations of the classical Blaschke-Santaló inequality. Related, we discuss an analogue of a conjecture due to K. Ball \cite{Ball-conjecture} in the multi-entry setting and establish a connection to the $j$-Santaló conjecture.
