[This is a question I'd asked on Yahoo! Answers some time ago which did not elicit any particularly helpful responses thereat.]
Both the thousand-armed Hehaya king Kārtavīryārjuna and the ten-headed Rākṣasa Rāvaṇa are said to have conquered the entire universe at some point, subduing even the gods in the heavens themselves; and each one of them was eventually defeated and killed by an avatāra [incarnation] of the god Viṣṇu [Vishnu]. Kārtavīryārjuna supposedly ruled the world, from his capital of Māhiṣmatī, for 86,000 years! Also he once captured and imprisoned Rāvaṇa for an entire year before Rāvaṇa's grandfather Pulastya brokered his grandson's release and Kārtavīryārjuna and Rāvaṇa became friends for life. So how can they both have ruled the universe if they lived in the same time-period (and especially considering the extraordinary length of Kārtavīryārjuna's reign)? Did they share the throne, or alternate their rule, at any point?
Since Kārtavīryārjuna was killed by Viṣṇu's 6th avatāra, Paraśurāma, while Rāvaṇa was killed by Viṣṇu's 7th avatāra, Rāma (or Rāmacandra), then eventually Rāvaṇa must have been emperor for a while after Kārtavīryārjuna's death. But what about when both emperors were alive, and friends?
And how does Kārtavīryārjuna's conquest of the universe fit in to the story about the foundation of the kingdom of Laṅkā, when Rāvaṇa's grandfather Sumali and Sumali's brothers Mali and Malyavan attacked Devāloka, the home of the gods, and were killed by Viṣṇu? Was Kārtavīryārjuna ruling over Devāloka at the time of the three brothers' attack?