토릭 특이점 유형의 Hausdorff 거리와 계량에 관하여
본 논문에서는 복소 사영 공간에서 토릭 특이점 유형의 공간에 대한 두 가지 계량, 즉 Darvas-Di Nezza-Lu 계량과 Hausdorff 계량을 비교하고, 이 두 계량이 동일한 위상을 유도함을 보여줍니다.
$L^p$-르장드르 변환과 말러 적분: 점근 및 포커-플랑크 열 흐름
본 논문에서는 볼록체에 대한 $L^p$-극성과 $L^p$-말러 부피의 개념을 함수로 확장하여 $L^p$-르장드르 변환과 $L^p$-말러 적분을 소개하고, 이를 통해 함수에 대한 $L^p$ 산탈로 부등식을 구하는 두 가지 방법을 제시합니다.
$L^p$-Legendre Transforms and Mahler Integrals for Convex Functions: Asymptotics, Connections to the Fokker-Planck Heat Flow, and a Functional $L^p$ Santaló Inequality
This paper introduces and explores the $L^p$-Legendre transform and $L^p$-Mahler integral, functional analogs of concepts in convex geometry, establishing their properties and connections to the Fokker-Planck heat flow, culminating in a functional $L^p$ Santaló inequality.
Construction of a Convex Body in ℝn (n ≥ 5) with a Unique Hyperplane Section Having a Coinciding Centroid
In dimensions five and higher, a convex body can be constructed such that there exists only one hyperplane passing through its centroid that also has a coinciding centroid with the section created by the hyperplane.
運河類與奇格集的關係
本文探討了凸體的體積與表面積之比值，特別關注於何時此比值的最大值會由與給定投影相同高度的圓柱體在極限情況下達到。
Canal Classes and Cheeger Sets: Characterizing Optimal Convex Body Shapes for a Given Projection
This mathematics paper investigates the geometric properties of convex bodies, specifically focusing on the relationship between their volume, surface area, and orthogonal projections. It disproves a conjecture about the optimal shape maximizing the ratio of volume to surface area for convex bodies sharing the same projection, and instead characterizes this optimal shape in terms of Cheeger sets.
行列空間におけるRogers--Brascamp--Lieb--Luttinger不等式
本論文では、行列空間における新しいタイプの対称化を用いて、古典的なRogers–Brascamp–Lieb–Luttinger不等式の一般化を証明しています。
Affine Quermassintegrals and Even Minkowski Valuations: Establishing Isoperimetric Inequalities for a Large Class of Operators
This article proves that a large class of geometric inequalities, including the classical relations between quermassintegrals and volume, can be strengthened to encompass all even Minkowski valuations with non-negative spherical Crofton distributions.
平面中卷積體體積之探討：橢圓體並非最大化體積的形狀
在平面上，對於任何固定的體積和卷積參數，橢圓體並非最大化卷積體體積的形狀，這與由佩蒂投影不等式所支配的極限情況形成對比。
C-偽錐的漸近理論
本文闡述了 C-偽錐的漸近特性，將其分解為 C-漸近集和 C-起始點的和，並以此為基礎，探討了加權體積、加權共體積和漸近加權共體積泛函的有限性，並提出了一個關於 C-偽錐的漸近布倫-閔可夫斯基不等式的開放性問題。
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