Question: Men who refused to believe in the formal surrender of Japan continued to stay where?

Context paragraphs:
Spring 1945 offensive in Italy: The Spring 1945 offensive in Italy, codenamed Operation Grapeshot, was the final Allied attack during the Italian Campaign in the final stages of the Second World War.  The attack into the Lombardy Plain by the 15th Allied Army Group started on 6 April 1945, ending on 2 May with the formal surrender of German forces in Italy.

Gau March of Brandenburg: The Gau Mark Brandenburg was formed in 1933 initially under the name Gau Kurmark in Nazi Germany initially as a district within the Free State of Prussia.  In 1935, Germany's constituent states were dissolved and the Gaus replaced the states and their responsibilities.  In 1940, Kurmark was renamed Mark Brandenburg.  The Gau was dissolved in 1945, following Allied Soviet occupation of the area and Germany's formal surrender in 1945.  After the war, the territory of the former Gau became part of the state of Brandenburg in East Germany except one of beyond Oder-Neisse line, which was given to People's Republic of Poland.  Most territories of it are divided between Germany's State of Brandenburg and Poland's Lubusz Voivodeship now.

Occupation of the Baltic states: The occupation of the Baltic states was the military occupation of the three Baltic states—Estonia, Latvia and Lithuania—by the Soviet Union under the auspices of the Molotov–Ribbentrop Pact on 14 June 1940 followed by their incorporation into the USSR as constituent republics, unrecognised by most Western powers.  On 22 June 1941 Nazi Germany attacked the USSR and within weeks occupied the Baltic territories.  In July 1941, the Baltic territory was incorporated into the "Reichskommissariat Ostland" of the Third Reich.  As a result of the Baltic Offensive of 1944, the Soviet Union recaptured most of the Baltic states and trapped the remaining German forces in the Courland pocket until their formal surrender in May 1945.  The Soviet "annexation occupation" ("Annexionsbesetzung " or occupation "sui generis") of the Baltic states lasted until August 1991, when the Baltic states regained independence.

Battle of Waxhaws: The Battle of Waxhaws (also known as the Waxhaws or Waxhaw massacre, and Buford's massacre) took place during the American Revolutionary War on May 29, 1780, near Lancaster, South Carolina, between a Continental Army force led by Abraham Buford and a mainly Loyalist force led by British officer Banastre Tarleton.  Buford refused an initial demand to surrender, but when his men were attacked by Tarleton's cavalry, many threw down their arms to surrender.  Buford apparently attempted to surrender.  However, the British commanding officer Tarleton was shot at during the truce, having his horse fall and trap him.  Loyalists and British troops were outraged at the breaking of the truce in this manner and proceeded to fall on the rebels.

Invasion of Guadeloupe (1759): The British expedition against Guadeloupe was a military action from January to May 1759, as part of the Seven Years' War.  A large British force had arrived in the West Indies, intending to seize French possessions.  After a six-month-long battle to capture Guadeloupe they finally received the formal surrender of the island, just days before a large French relief force arrived under Admiral Maximin de Bompart.

Battle of Java (1942): The Battle of Java (Invasion of Java, Operation J) was a battle of the Pacific theatre of World War II.  It occurred on the island of Java from 28 February – 12 March 1942.  It involved forces from the Empire of Japan, which invaded on 28 February 1942, and Allied personnel.  Allied commanders signed a formal surrender at Japanese headquarters at Bandung on 12 March.

Miller v. Davis: Miller v. Davis is a federal lawsuit in the United States regarding the issuance of marriage licenses to same-sex couples.  After the U.S. Supreme Court legalized same-sex marriage nationwide on June 26, 2015, the county clerk of Rowan County, Kentucky, Kim Davis, refused to issue marriage licenses to any couple to avoid issuing them to same-sex couples, citing her religious beliefs.  She also refused to allow her deputies to issue the licenses, as they would still bear her title and name.  On August 12, 2015, U.S. District Judge David L. Bunning ordered Davis to issue marriage licenses to all couples.  He stayed his ruling until August 31, at her request, while she sought a stay pending appeal.  A federal appeals court denied the stay, followed by the Supreme Court who also refused to stay the ruling.  On September 3, Judge Bunning ordered Davis jailed for contempt of court until she complies with the order.  Davis was released on September 8, following her deputy clerks issuing marriage licenses to the plaintiffs during her jailing.  On September 14, Davis returned to work where she is not standing in the way of her clerks issuing licenses, though she questions their validity.  The case was dismissed as moot on April 19, 2016.

Resistance (military): In military terminology, resistance or organised resistance refers to the ability of a military unit to continue to oppose an attack.  Resistance ends when a unit surrenders, when all members of a unit are killed or captured, or when a unit disperses.  The term is used in the phrase "organized resistance has ceased" to describe the end of a battle or campaign when no formal surrender occurs after a unit is defeated.  The term also occurs in the phrase "pocket of resistance."

Battle of Luzon: The Battle of Luzon, fought 9 January – 15 August 1945, was a land battle of the Pacific Theater of Operations of World War II by the Allied forces of the U.S., its colony the Philippines, and allies against forces of the Empire of Japan.  The battle resulted in a U.S. and Filipino victory.  The Allies had taken control of all strategically and economically important locations of Luzon by March 1945, although pockets of Japanese resistance held out in the mountains until the unconditional surrender of Japan.  While not the highest in U.S. casualties, it is the highest net casualty battle U.S. forces fought in World War II, with 192,000 to 205,000 Japanese combatants dead (mostly from starvation and disease), 10,000 American combatants killed, and between 120,000 to 140,000 Filipino civilians and combatants killed.

Japanese holdout: Japanese holdouts (残留日本兵 , Zanryū nipponhei , "remaining Japanese soldiers") or stragglers were Japanese soldiers in the Pacific Theatre who, after the August 1945 surrender of Japan ending World War II, either adamantly doubted the veracity of the formal surrender due to dogmatic militaristic principles, or simply were not aware of it because communications had been cut off by Allied advances.

Supporting paragraphs: Battle of Luzon Japanese holdout
Answer: in the mountains