TY - JOUR
T1 - Optimal Finsler–Hadwiger Inequalities
AU - Bogosel, Beniamin
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
PY - 2025/5/1
Y1 - 2025/5/1
N2 - Various inequalities exist between the area of a triangle, the perimeter squared (a+b+c)2 and the isoperimetric deficit Q=(a-b)2+(b-c)2+(c-a)2. The direct and reverse Finsler–Hadwiger inequalities correspond to the best linear inequalities between the three quantities mentioned above. In this paper, the sharpest inequalities between these three quantities are found explicitly. The techniques used involve Blaschke-Santaló diagrams and constrained optimization problems.
AB - Various inequalities exist between the area of a triangle, the perimeter squared (a+b+c)2 and the isoperimetric deficit Q=(a-b)2+(b-c)2+(c-a)2. The direct and reverse Finsler–Hadwiger inequalities correspond to the best linear inequalities between the three quantities mentioned above. In this paper, the sharpest inequalities between these three quantities are found explicitly. The techniques used involve Blaschke-Santaló diagrams and constrained optimization problems.
KW - Blaschke-Santaló diagram
KW - Finsler–Hadwiger inequalities
KW - Inequalities in triangles
KW - quantitative isoperimetric inequalities
UR - https://www.scopus.com/pages/publications/105002743053
U2 - 10.1007/s00025-025-02405-6
DO - 10.1007/s00025-025-02405-6
M3 - Article
AN - SCOPUS:105002743053
SN - 1422-6383
VL - 80
JO - Results in Mathematics
JF - Results in Mathematics
IS - 3
M1 - 88
ER -