@article{MTMT:32982788,
	title = {Boundary-Rigidity of Projective Metrics and the Geodesic X-Ray Transform},
	url = {https://m2.mtmt.hu/api/publication/32982788},
	author = {Kurusa, Árpád and Ódor, Tibor},
	doi = {10.1007/s12220-022-00942-y},
	journal-iso = {J GEOM ANAL},
	journal = {JOURNAL OF GEOMETRIC ANALYSIS},
	volume = {32},
	unique-id = {32982788},
	issn = {1050-6926},
	abstract = {We prove that given a compact convex non-empty domain M in the plane, a function delta: partial derivative M x partial derivative M -> R+ can be extended to a projective metric d on M if and only if delta(P, R) +delta(Q, S) - delta(P, S) - delta(Q, R) > 0 for any convex quadrangle square(PQRS) inscribed in partial derivative M. Moreover, this extension is unique.},
	keywords = {Rigidity; X-ray transform; projective metric},
	year = {2022},
	eissn = {1559-002X},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:31371509,
	title = {Finding Needles in a Haystack},
	url = {https://m2.mtmt.hu/api/publication/31371509},
	author = {Kurusa, Árpád},
	doi = {10.1007/s00454-020-00217-9},
	journal-iso = {DISCRETE COMPUT GEOM},
	journal = {DISCRETE AND COMPUTATIONAL GEOMETRY},
	volume = {65},
	unique-id = {31371509},
	issn = {0179-5376},
	abstract = {Convex polygons are distinguishable among the piecewise $C^\infty$ convex domains by comparing their visual angle functions on any surrounding circle. This is a consequence of our main result, that every segment in a $C^\infty$ multi\-curve can be reconstructed from the masking function of the multicurve given on any surrounding circle.},
	year = {2021},
	eissn = {1432-0444},
	pages = {470-475},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:31290416,
	title = {Curvature in Hilbert Geometries},
	url = {https://m2.mtmt.hu/api/publication/31290416},
	author = {Kurusa, Árpád},
	journal = {International Journal of Geometry},
	volume = {9},
	unique-id = {31290416},
	issn = {2247-9880},
	year = {2020},
	eissn = {2247-9880},
	pages = {85-94},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:31681702,
	title = {Euler's ratio-sum theorem revisited},
	url = {https://m2.mtmt.hu/api/publication/31681702},
	author = {Kurusa, Árpád and Kozma, József},
	journal-iso = {Glob. J. Adv. Res. Cl. Mod. Geom.},
	journal = {GLOBAL JOURNAL OF ADVANCED RESEARCH ON CLASSICAL AND MODERN GEOMETRIES},
	volume = {9},
	unique-id = {31681702},
	year = {2020},
	eissn = {2284-5569},
	pages = {83-89},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:31407382,
	title = {Tiling a circular disc with congruent pieces},
	url = {https://m2.mtmt.hu/api/publication/31407382},
	author = {Kurusa, Árpád and Lángi, Zsolt and Vígh, Viktor},
	doi = {10.1007/s00009-020-01595-3},
	journal-iso = {MEDITERR J MATH},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {17},
	unique-id = {31407382},
	issn = {1660-5446},
	abstract = {In this note we prove that any monohedral tiling of the closed circular unit disc with $k \leq 3$ topological discs as tiles has a $k$-fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain the center, and the first step towards answering a question of Stein appearing in the problem book of Croft, Falconer and Guy in 1994.},
	year = {2020},
	eissn = {1660-5454},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606; Lángi, Zsolt/0000-0002-5999-5343}
}

@article{MTMT:30795464,
	title = {Hilbert geometries with Riemannian points},
	url = {https://m2.mtmt.hu/api/publication/30795464},
	author = {Kurusa, Árpád},
	doi = {10.1007/s10231-019-00901-5},
	journal-iso = {ANN MAT PUR APPL},
	journal = {ANNALI DI MATEMATICA PURA ED APPLICATA},
	volume = {199},
	unique-id = {30795464},
	issn = {0373-3114},
	year = {2020},
	eissn = {1618-1891},
	pages = {809-820},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:30358648,
	title = {Euler’s ratio-sum formula in projective-metric spaces},
	url = {https://m2.mtmt.hu/api/publication/30358648},
	author = {Kurusa, Árpád and Kozma, József},
	doi = {10.1007/s13366-018-0422-6},
	journal-iso = {BEITR ALGEBR GEOM},
	journal = {BEITRAGE ZUR ALGEBRA UND GEOMETRIE},
	volume = {60},
	unique-id = {30358648},
	issn = {0138-4821},
	abstract = {We prove that Euler’s ratio-sum formula is valid in a projective-metric space if and only if it is either elliptic, hyperbolic, or Minkowskian.},
	year = {2019},
	eissn = {2191-0383},
	pages = {379-390},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:30359280,
	title = {A convex combinatorial property of compact sets in the plane and its roots in lattice theory},
	url = {https://m2.mtmt.hu/api/publication/30359280},
	author = {Czédli, Gábor and Kurusa, Árpád},
	journal-iso = {CAT GEN ALGEBR STRUCT APPL},
	journal = {CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS},
	volume = {11},
	unique-id = {30359280},
	issn = {2345-5853},
	abstract = {K. Adaricheva and M. Bolat have recently proved that if $U_0$ and $U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $j\in\{0,1,2\}$ and $k\in\{0,1\}$ such that $U_{1−k}$ is included in the convex hull of $U_k\cup(\{A_0,A_1,A_2\}∖setminus\{A_j\})$. One could say disks instead of circles. Here we prove the existence of such a $j$ and $k$ for the more general case where $U_0$ and $U_1$ are compact sets in the plane such that $U_1$ is obtained from $U_0$ by a positive homothety or by a translation. Also, we give a short survey to show how lattice theoretical antecedents, including a series of papers on planar semimodular lattices by G. Gr\"atzer and E. Knapp, lead to our result.},
	year = {2019},
	eissn = {2345-5861},
	pages = {57-92},
	orcid-numbers = {Czédli, Gábor/0000-0001-9990-3573; Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:30852537,
	title = {Ceva’s and Menelaus’ theorems in projective-metric spaces},
	url = {https://m2.mtmt.hu/api/publication/30852537},
	author = {Kurusa, Árpád},
	doi = {10.1007/s00022-019-0495-x},
	journal-iso = {J GEOM},
	journal = {JOURNAL OF GEOMETRY},
	volume = {110},
	unique-id = {30852537},
	issn = {0047-2468},
	abstract = {We prove that Ceva’s and Menelaus’ theorems are valid in a projective-metric space if and only if the space is any of the elliptic geometry, the hyperbolic geometry, or the Minkowski geometries. © 2019, The Author(s).},
	keywords = {Triangle; Minkowski geometry; Ellipses; Hilbert geometry; Projective metrics; size-ratio},
	year = {2019},
	eissn = {1420-8997},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}

@article{MTMT:3424053,
	title = {Conics in Minkowski geometries},
	url = {https://m2.mtmt.hu/api/publication/3424053},
	author = {Kurusa, Árpád},
	doi = {10.1007/s00010-018-0592-1},
	journal-iso = {AEQUATIONES MATH},
	journal = {AEQUATIONES MATHEMATICAE},
	volume = {92},
	unique-id = {3424053},
	issn = {0001-9054},
	year = {2018},
	eissn = {1420-8903},
	pages = {949-961},
	orcid-numbers = {Kurusa, Árpád/0000-0003-3113-9606}
}