What are the historical issues of Changbai Mountain (called Baektou Mountain in Korea)?

Changbai Mountain is the boundary mountain between China and North Korea. There are various arguments circulating on the Chinese Internet that "the Chinese Communist Party uses the Chinese homeland to win the favor of other countries". The source is unknown. One of them is that "Baekdu Mountain was originally unique to China before the 1960s. When China and North Korea demarcated the border in the 1960s, Give half to North Korea.” Some people in South Korea claim that it is South Korean territory, but currently neither South Korean nor North Korean officials have a dispute over the territorial boundary. On January 31, 2007, at the Winter Asian Games held in Changchun City, South Korean athletes won the runner-up in the women's short track speed skating 3,000-meter relay. On the podium, they suddenly displayed a slogan: "Baekdu Mountain is our territory." The move caused a diplomatic turmoil, with the Chinese Ministry of Foreign Affairs immediately protesting and South Korean officials expressing "regret" but not apologizing. After the incident, Chinese netizens protested. However, the relevant news was handled in a low-key manner by the Chinese government, while South Korean media generally supported the athletes' actions. But in fact, this place is the same border between China and North Korea, and South Korea is not a border country. There is no solid reason. Moreover, although Changbai Mountain is the claimed birthplace of the Korean nation, it is also the birthplace of Manchu mythology, so the statement that "Baektu Mountain belongs to Korea" has no evidence at all and is purely self-proclaimed.